id sid tid token lemma pos ejpam-6732 1 1 european european PROPN ejpam-6732 1 2 journal journal PROPN ejpam-6732 1 3 of of ADP ejpam-6732 1 4 pure pure ADJ ejpam-6732 1 5 and and CCONJ ejpam-6732 1 6 applied applied ADJ ejpam-6732 1 7 mathematics mathematic NOUN ejpam-6732 1 8 2025 2025 NUM ejpam-6732 1 9 , , PUNCT ejpam-6732 1 10 vol vol NOUN ejpam-6732 1 11 . . PROPN ejpam-6732 1 12 18 18 NUM ejpam-6732 1 13 , , PUNCT ejpam-6732 1 14 issue issue NOUN ejpam-6732 1 15 4 4 NUM ejpam-6732 1 16 , , PUNCT ejpam-6732 1 17 article article NOUN ejpam-6732 1 18 number number NOUN ejpam-6732 1 19 6732 6732 NUM ejpam-6732 1 20 issn issn PROPN ejpam-6732 1 21 1307 1307 NUM ejpam-6732 1 22 - - SYM ejpam-6732 1 23 5543 5543 NUM ejpam-6732 1 24 – – PUNCT ejpam-6732 1 25 ejpam.com ejpam.com X ejpam-6732 1 26 published publish VERB ejpam-6732 1 27 by by ADP ejpam-6732 1 28 new new PROPN ejpam-6732 1 29 york york PROPN ejpam-6732 1 30 business business PROPN ejpam-6732 1 31 global global PROPN ejpam-6732 1 32 some some DET ejpam-6732 1 33 new new ADJ ejpam-6732 1 34 boundedness boundedness NOUN ejpam-6732 1 35 results result NOUN ejpam-6732 1 36 for for ADP ejpam-6732 1 37 variable variable ADJ ejpam-6732 1 38 marcinkiewicz marcinkiewicz ADJ ejpam-6732 1 39 fractional fractional ADJ ejpam-6732 1 40 integral integral ADJ ejpam-6732 1 41 operator operator NOUN ejpam-6732 1 42 on on ADP ejpam-6732 1 43 herz herz PROPN ejpam-6732 1 44 - - PUNCT ejpam-6732 1 45 morrey morrey NOUN ejpam-6732 1 46 - - PUNCT ejpam-6732 1 47 hardy hardy ADJ ejpam-6732 1 48 spaces space NOUN ejpam-6732 1 49 babar babar PROPN ejpam-6732 1 50 sultan1 sultan1 PROPN ejpam-6732 1 51 , , PUNCT ejpam-6732 1 52 amjad amjad PROPN ejpam-6732 1 53 hussain1,∗ hussain1,∗ PROPN ejpam-6732 1 54 , , PUNCT ejpam-6732 1 55 mehvish mehvish PROPN ejpam-6732 1 56 sultan2 sultan2 NOUN ejpam-6732 1 57 , , PUNCT ejpam-6732 1 58 ioan ioan PROPN ejpam-6732 1 59 - - PUNCT ejpam-6732 1 60 lucian lucian PROPN ejpam-6732 1 61 popa3,4,∗ popa3,4,∗ PROPN ejpam-6732 1 62 1 1 NUM ejpam-6732 1 63 department department NOUN ejpam-6732 1 64 of of ADP ejpam-6732 1 65 mathematics mathematic NOUN ejpam-6732 1 66 , , PUNCT ejpam-6732 1 67 quaid quaid PROPN ejpam-6732 1 68 - - PUNCT ejpam-6732 1 69 i i PROPN ejpam-6732 1 70 - - PUNCT ejpam-6732 1 71 azam azam PROPN ejpam-6732 1 72 university university PROPN ejpam-6732 1 73 , , PUNCT ejpam-6732 1 74 islamabad islamabad PROPN ejpam-6732 1 75 45320 45320 NUM ejpam-6732 1 76 , , PUNCT ejpam-6732 1 77 pakistan pakistan PROPN ejpam-6732 1 78 2 2 NUM ejpam-6732 1 79 department department NOUN ejpam-6732 1 80 of of ADP ejpam-6732 1 81 mathematics mathematic NOUN ejpam-6732 1 82 , , PUNCT ejpam-6732 1 83 capital capital NOUN ejpam-6732 1 84 university university PROPN ejpam-6732 1 85 of of ADP ejpam-6732 1 86 science science NOUN ejpam-6732 1 87 and and CCONJ ejpam-6732 1 88 technology technology NOUN ejpam-6732 1 89 , , PUNCT ejpam-6732 1 90 islamabad islamabad PROPN ejpam-6732 1 91 , , PUNCT ejpam-6732 1 92 pakistan pakistan PROPN ejpam-6732 1 93 3 3 NUM ejpam-6732 1 94 department department NOUN ejpam-6732 1 95 of of ADP ejpam-6732 1 96 computing computing NOUN ejpam-6732 1 97 , , PUNCT ejpam-6732 1 98 mathematics mathematic NOUN ejpam-6732 1 99 and and CCONJ ejpam-6732 1 100 electronics electronic NOUN ejpam-6732 1 101 , , PUNCT ejpam-6732 1 102 “ " PUNCT ejpam-6732 1 103 1 1 NUM ejpam-6732 1 104 decembrie decembrie NOUN ejpam-6732 1 105 1918 1918 NUM ejpam-6732 1 106 ” " PUNCT ejpam-6732 1 107 university university PROPN ejpam-6732 1 108 of of ADP ejpam-6732 1 109 alba alba PROPN ejpam-6732 1 110 iulia iulia PROPN ejpam-6732 1 111 , , PUNCT ejpam-6732 1 112 510009 510009 NUM ejpam-6732 1 113 alba alba NOUN ejpam-6732 1 114 iulia iulia PROPN ejpam-6732 1 115 , , PUNCT ejpam-6732 1 116 romania romania PROPN ejpam-6732 1 117 4 4 NUM ejpam-6732 1 118 faculty faculty NOUN ejpam-6732 1 119 of of ADP ejpam-6732 1 120 mathematics mathematic NOUN ejpam-6732 1 121 and and CCONJ ejpam-6732 1 122 computer computer NOUN ejpam-6732 1 123 science science NOUN ejpam-6732 1 124 , , PUNCT ejpam-6732 1 125 transilvania transilvania PROPN ejpam-6732 1 126 university university PROPN ejpam-6732 1 127 of of ADP ejpam-6732 1 128 brasov brasov NOUN ejpam-6732 1 129 , , PUNCT ejpam-6732 1 130 iuliu iuliu PROPN ejpam-6732 1 131 maniu maniu PROPN ejpam-6732 1 132 street street PROPN ejpam-6732 1 133 50 50 NUM ejpam-6732 1 134 , , PUNCT ejpam-6732 1 135 500091 500091 NUM ejpam-6732 1 136 brasov brasov NOUN ejpam-6732 1 137 , , PUNCT ejpam-6732 1 138 romania romania PROPN ejpam-6732 1 139 abstract abstract NOUN ejpam-6732 1 140 . . PUNCT ejpam-6732 2 1 in in ADP ejpam-6732 2 2 this this DET ejpam-6732 2 3 paper paper NOUN ejpam-6732 2 4 , , PUNCT ejpam-6732 2 5 we we PRON ejpam-6732 2 6 define define VERB ejpam-6732 2 7 the the DET ejpam-6732 2 8 idea idea NOUN ejpam-6732 2 9 of of ADP ejpam-6732 2 10 herz herz PROPN ejpam-6732 2 11 - - PUNCT ejpam-6732 2 12 morrey morrey NOUN ejpam-6732 2 13 - - PUNCT ejpam-6732 2 14 hardy hardy ADJ ejpam-6732 2 15 spaces space NOUN ejpam-6732 2 16 by by ADP ejpam-6732 2 17 using use VERB ejpam-6732 2 18 variable variable ADJ ejpam-6732 2 19 herzmorrey herzmorrey NOUN ejpam-6732 2 20 spaces space NOUN ejpam-6732 2 21 and and CCONJ ejpam-6732 2 22 hardy hardy ADJ ejpam-6732 2 23 spaces space NOUN ejpam-6732 2 24 . . PUNCT ejpam-6732 3 1 then then ADV ejpam-6732 3 2 we we PRON ejpam-6732 3 3 give give VERB ejpam-6732 3 4 the the DET ejpam-6732 3 5 atomic atomic ADJ ejpam-6732 3 6 characterization characterization NOUN ejpam-6732 3 7 of of ADP ejpam-6732 3 8 these these DET ejpam-6732 3 9 spaces space NOUN ejpam-6732 3 10 by by ADP ejpam-6732 3 11 using use VERB ejpam-6732 3 12 the the DET ejpam-6732 3 13 grand grand ADJ ejpam-6732 3 14 maximal maximal ADJ ejpam-6732 3 15 function function NOUN ejpam-6732 3 16 . . PUNCT ejpam-6732 4 1 then then ADV ejpam-6732 4 2 our our PRON ejpam-6732 4 3 main main ADJ ejpam-6732 4 4 objective objective NOUN ejpam-6732 4 5 is be AUX ejpam-6732 4 6 to to PART ejpam-6732 4 7 prove prove VERB ejpam-6732 4 8 the the DET ejpam-6732 4 9 boundedness boundedness NOUN ejpam-6732 4 10 of of ADP ejpam-6732 4 11 higher high ADJ ejpam-6732 4 12 order order NOUN ejpam-6732 4 13 commutators commutator NOUN ejpam-6732 4 14 of of ADP ejpam-6732 4 15 variable variable ADJ ejpam-6732 4 16 marcinkiewicz marcinkiewicz ADJ ejpam-6732 4 17 fractional fractional ADJ ejpam-6732 4 18 integral integral ADJ ejpam-6732 4 19 operator operator NOUN ejpam-6732 4 20 on on ADP ejpam-6732 4 21 herz herz PROPN ejpam-6732 4 22 - - PUNCT ejpam-6732 4 23 morrey morrey NOUN ejpam-6732 4 24 - - PUNCT ejpam-6732 4 25 hardy hardy ADJ ejpam-6732 4 26 spaces space NOUN ejpam-6732 4 27 where where SCONJ ejpam-6732 4 28 the the DET ejpam-6732 4 29 exponents exponent NOUN ejpam-6732 4 30 defining define VERB ejpam-6732 4 31 these these DET ejpam-6732 4 32 spaces space NOUN ejpam-6732 4 33 are be AUX ejpam-6732 4 34 variable variable ADJ ejpam-6732 4 35 . . PUNCT ejpam-6732 5 1 these these DET ejpam-6732 5 2 results result NOUN ejpam-6732 5 3 also also ADV ejpam-6732 5 4 hold hold VERB ejpam-6732 5 5 for for ADP ejpam-6732 5 6 variable variable ADJ ejpam-6732 5 7 herz herz ADJ ejpam-6732 5 8 - - PUNCT ejpam-6732 5 9 hardy hardy ADJ ejpam-6732 5 10 spaces space NOUN ejpam-6732 5 11 . . PUNCT ejpam-6732 6 1 the the DET ejpam-6732 6 2 higher high ADJ ejpam-6732 6 3 order order NOUN ejpam-6732 6 4 commutators commutator NOUN ejpam-6732 6 5 of of ADP ejpam-6732 6 6 variable variable ADJ ejpam-6732 6 7 marcinkiewicz marcinkiewicz ADJ ejpam-6732 6 8 fractional fractional ADJ ejpam-6732 6 9 integral integral ADJ ejpam-6732 6 10 operator operator NOUN ejpam-6732 6 11 is be AUX ejpam-6732 6 12 the the DET ejpam-6732 6 13 generalization generalization NOUN ejpam-6732 6 14 of of ADP ejpam-6732 6 15 marcinkiewicz marcinkiewicz ADJ ejpam-6732 6 16 integral integral ADJ ejpam-6732 6 17 operators operator NOUN ejpam-6732 6 18 , , PUNCT ejpam-6732 6 19 variable variable ADJ ejpam-6732 6 20 marcinkiewicz marcinkiewicz ADJ ejpam-6732 6 21 fractional fractional ADJ ejpam-6732 6 22 integral integral ADJ ejpam-6732 6 23 operator operator NOUN ejpam-6732 6 24 and and CCONJ ejpam-6732 6 25 commutators commutator NOUN ejpam-6732 6 26 on on ADP ejpam-6732 6 27 marcinkiewicz marcinkiewicz ADJ ejpam-6732 6 28 fractional fractional ADJ ejpam-6732 6 29 integral integral ADJ ejpam-6732 6 30 operators operator NOUN ejpam-6732 6 31 , , PUNCT ejpam-6732 6 32 so so SCONJ ejpam-6732 6 33 these these DET ejpam-6732 6 34 proofs proof NOUN ejpam-6732 6 35 generalize generalize VERB ejpam-6732 6 36 some some DET ejpam-6732 6 37 previous previous ADJ ejpam-6732 6 38 results result NOUN ejpam-6732 6 39 . . PUNCT ejpam-6732 7 1 2020 2020 NUM ejpam-6732 7 2 mathematics mathematic NOUN ejpam-6732 7 3 subject subject NOUN ejpam-6732 7 4 classifications classification NOUN ejpam-6732 7 5 : : PUNCT ejpam-6732 7 6 42b20 42b20 NUM ejpam-6732 7 7 , , PUNCT ejpam-6732 7 8 47b38 47b38 DET ejpam-6732 7 9 key key ADJ ejpam-6732 7 10 words word NOUN ejpam-6732 7 11 and and CCONJ ejpam-6732 7 12 phrases phrase NOUN ejpam-6732 7 13 : : PUNCT ejpam-6732 7 14 bmo bmo PROPN ejpam-6732 7 15 spaces space NOUN ejpam-6732 7 16 , , PUNCT ejpam-6732 7 17 marcinkiewicz marcinkiewicz ADJ ejpam-6732 7 18 fractional fractional ADJ ejpam-6732 7 19 integral integral ADJ ejpam-6732 7 20 , , PUNCT ejpam-6732 7 21 herz herz ADJ ejpam-6732 7 22 - - PUNCT ejpam-6732 7 23 morrey morrey NOUN ejpam-6732 7 24 - - PUNCT ejpam-6732 7 25 hardy hardy ADJ ejpam-6732 7 26 spaces space NOUN ejpam-6732 7 27 1 1 NUM ejpam-6732 7 28 . . PUNCT ejpam-6732 7 29 introduction introduction NOUN ejpam-6732 7 30 and and CCONJ ejpam-6732 7 31 preliminaries preliminary NOUN ejpam-6732 7 32 let let VERB ejpam-6732 7 33 e e PRON ejpam-6732 7 34 be be AUX ejpam-6732 7 35 an an DET ejpam-6732 7 36 open open ADJ ejpam-6732 7 37 set set NOUN ejpam-6732 7 38 in in ADP ejpam-6732 7 39 rn rn PROPN ejpam-6732 7 40 , , PUNCT ejpam-6732 7 41 consider consider VERB ejpam-6732 7 42 a a DET ejpam-6732 7 43 measurable measurable ADJ ejpam-6732 7 44 function function NOUN ejpam-6732 7 45 p p X ejpam-6732 7 46 ( ( PUNCT ejpam-6732 7 47 · · PUNCT ejpam-6732 7 48 ) ) PUNCT ejpam-6732 7 49 : : PUNCT ejpam-6732 8 1 e e X ejpam-6732 8 2 → → PUNCT ejpam-6732 8 3 [ [ X ejpam-6732 8 4 1,∞ 1,∞ NUM ejpam-6732 8 5 ) ) PUNCT ejpam-6732 8 6 . . PUNCT ejpam-6732 9 1 the the DET ejpam-6732 9 2 conjugate conjugate ADJ ejpam-6732 9 3 exponent exponent NOUN ejpam-6732 9 4 denoted denote VERB ejpam-6732 9 5 by by ADP ejpam-6732 9 6 p′ p′ PROPN ejpam-6732 9 7 ( ( PUNCT ejpam-6732 9 8 · · PUNCT ejpam-6732 9 9 ) ) PUNCT ejpam-6732 9 10 , , PUNCT ejpam-6732 9 11 is be AUX ejpam-6732 9 12 defined define VERB ejpam-6732 9 13 as as ADP ejpam-6732 9 14 p′ p′ NOUN ejpam-6732 9 15 ( ( PUNCT ejpam-6732 9 16 · · PUNCT ejpam-6732 9 17 ) ) PUNCT ejpam-6732 10 1 = = PRON ejpam-6732 10 2 p(·)/(p(·)− p(·)/(p(·)− NOUN ejpam-6732 10 3 1 1 NUM ejpam-6732 10 4 ) ) PUNCT ejpam-6732 10 5 . . PUNCT ejpam-6732 11 1 the the DET ejpam-6732 11 2 set set NOUN ejpam-6732 11 3 p(e p(e NOUN ejpam-6732 11 4 ) ) PUNCT ejpam-6732 11 5 comprises comprise VERB ejpam-6732 11 6 all all DET ejpam-6732 11 7 functions function NOUN ejpam-6732 11 8 p p X ejpam-6732 11 9 ( ( PUNCT ejpam-6732 11 10 · · PUNCT ejpam-6732 11 11 ) ) PUNCT ejpam-6732 11 12 : : PUNCT ejpam-6732 12 1 e e X ejpam-6732 12 2 → → PUNCT ejpam-6732 12 3 [ [ X ejpam-6732 12 4 1,∞ 1,∞ NUM ejpam-6732 12 5 ) ) PUNCT ejpam-6732 12 6 . . PUNCT ejpam-6732 13 1 we we PRON ejpam-6732 13 2 suppose suppose VERB ejpam-6732 13 3 that that SCONJ ejpam-6732 13 4 1 1 NUM ejpam-6732 13 5 ≤ ≤ NUM ejpam-6732 13 6 p−(e p−(e NOUN ejpam-6732 13 7 ) ) PUNCT ejpam-6732 13 8 ≤ ≤ NUM ejpam-6732 13 9 p(x p(x PROPN ejpam-6732 13 10 ) ) PUNCT ejpam-6732 13 11 ≤ ≤ NUM ejpam-6732 13 12 p+(e p+(e PROPN ejpam-6732 13 13 ) ) PUNCT ejpam-6732 13 14 < < X ejpam-6732 14 1 ∞ ∞ PROPN ejpam-6732 14 2 , , PUNCT ejpam-6732 14 3 ( ( PUNCT ejpam-6732 14 4 1.1 1.1 NUM ejpam-6732 14 5 ) ) PUNCT ejpam-6732 14 6 ∗corresponding ∗corresponde VERB ejpam-6732 14 7 author author NOUN ejpam-6732 14 8 . . PUNCT ejpam-6732 15 1 ∗corresponding ∗corresponde VERB ejpam-6732 15 2 author author NOUN ejpam-6732 15 3 . . PUNCT ejpam-6732 16 1 doi doi NOUN ejpam-6732 16 2 : : PUNCT ejpam-6732 16 3 https://doi.org/10.29020/nybg.ejpam.v18i4.6732 https://doi.org/10.29020/nybg.ejpam.v18i4.6732 ADJ ejpam-6732 16 4 email email NOUN ejpam-6732 16 5 addresses address NOUN ejpam-6732 16 6 : : PUNCT ejpam-6732 16 7 babarsultan40@yahoo.com babarsultan40@yahoo.com X ejpam-6732 16 8 ( ( PUNCT ejpam-6732 16 9 b. b. PROPN ejpam-6732 16 10 sultan sultan PROPN ejpam-6732 16 11 ) ) PUNCT ejpam-6732 16 12 , , PUNCT ejpam-6732 16 13 a.hussain@qau.edu.pk a.hussain@qau.edu.pk PROPN ejpam-6732 16 14 ( ( PUNCT ejpam-6732 16 15 a. a. NOUN ejpam-6732 16 16 hussain hussain PROPN ejpam-6732 16 17 ) ) PUNCT ejpam-6732 16 18 , , PUNCT ejpam-6732 16 19 mehvishsultanbaz@gmail.com mehvishsultanbaz@gmail.com X ejpam-6732 16 20 ( ( PUNCT ejpam-6732 16 21 m. m. NOUN ejpam-6732 16 22 sultan sultan PROPN ejpam-6732 16 23 ) ) PUNCT ejpam-6732 16 24 , , PUNCT ejpam-6732 16 25 lucian.popa@uab.ro lucian.popa@uab.ro NOUN ejpam-6732 16 26 ( ( PUNCT ejpam-6732 16 27 i.-l i.-l NOUN ejpam-6732 16 28 . . PUNCT ejpam-6732 17 1 popa popa ADJ ejpam-6732 17 2 ) ) PUNCT ejpam-6732 17 3 https://www.ejpam.com https://www.ejpam.com NOUN ejpam-6732 18 1 1 1 NUM ejpam-6732 18 2 copyright copyright NOUN ejpam-6732 18 3 : : PUNCT ejpam-6732 18 4 © © PROPN ejpam-6732 18 5 2025 2025 NUM ejpam-6732 18 6 the the DET ejpam-6732 18 7 author(s author(s NOUN ejpam-6732 18 8 ) ) PUNCT ejpam-6732 18 9 . . PUNCT ejpam-6732 19 1 ( ( PUNCT ejpam-6732 19 2 cc cc NOUN ejpam-6732 19 3 by by ADP ejpam-6732 19 4 - - PUNCT ejpam-6732 19 5 nc nc PROPN ejpam-6732 19 6 4.0 4.0 NUM ejpam-6732 19 7 ) ) PUNCT ejpam-6732 19 8 b. b. PROPN ejpam-6732 19 9 sultan sultan PROPN ejpam-6732 19 10 et et PROPN ejpam-6732 19 11 al al PROPN ejpam-6732 19 12 . . PUNCT ejpam-6732 19 13 / / SYM ejpam-6732 19 14 eur eur PROPN ejpam-6732 19 15 . . PUNCT ejpam-6732 20 1 j. j. PROPN ejpam-6732 20 2 pure pure PROPN ejpam-6732 20 3 appl appl PROPN ejpam-6732 20 4 . . PROPN ejpam-6732 20 5 math math PROPN ejpam-6732 20 6 , , PUNCT ejpam-6732 20 7 18 18 NUM ejpam-6732 20 8 ( ( PUNCT ejpam-6732 20 9 4 4 NUM ejpam-6732 20 10 ) ) PUNCT ejpam-6732 20 11 ( ( PUNCT ejpam-6732 20 12 2025 2025 NUM ejpam-6732 20 13 ) ) PUNCT ejpam-6732 20 14 , , PUNCT ejpam-6732 20 15 6732 6732 NUM ejpam-6732 20 16 2 2 NUM ejpam-6732 20 17 of of ADP ejpam-6732 20 18 20 20 NUM ejpam-6732 20 19 such such ADJ ejpam-6732 20 20 that that DET ejpam-6732 20 21 p− p− NOUN ejpam-6732 20 22 = = PUNCT ejpam-6732 20 23 ess ess PROPN ejpam-6732 20 24 inf inf PROPN ejpam-6732 20 25 { { PUNCT ejpam-6732 20 26 p(x p(x PROPN ejpam-6732 20 27 ) ) PUNCT ejpam-6732 20 28 : : PUNCT ejpam-6732 21 1 x x PUNCT ejpam-6732 21 2 ∈ ∈ NOUN ejpam-6732 21 3 e e X ejpam-6732 21 4 } } PUNCT ejpam-6732 21 5 > > X ejpam-6732 21 6 1 1 NUM ejpam-6732 21 7 , , PUNCT ejpam-6732 21 8 p+ p+ X ejpam-6732 21 9 = = SYM ejpam-6732 21 10 ess ess PROPN ejpam-6732 21 11 sup sup PROPN ejpam-6732 21 12 { { PUNCT ejpam-6732 21 13 p(x p(x PROPN ejpam-6732 21 14 ) ) PUNCT ejpam-6732 21 15 : : PUNCT ejpam-6732 21 16 x x X ejpam-6732 21 17 ∈ ∈ NOUN ejpam-6732 21 18 e e X ejpam-6732 21 19 } } PUNCT ejpam-6732 21 20 < < X ejpam-6732 21 21 ∞. ∞. PROPN ejpam-6732 21 22 we we PRON ejpam-6732 21 23 use use VERB ejpam-6732 21 24 the the DET ejpam-6732 21 25 notation notation NOUN ejpam-6732 21 26 lp(·)(e lp(·)(e PROPN ejpam-6732 21 27 ) ) PUNCT ejpam-6732 21 28 to to PART ejpam-6732 21 29 represent represent VERB ejpam-6732 21 30 the the DET ejpam-6732 21 31 space space NOUN ejpam-6732 21 32 of of ADP ejpam-6732 21 33 all all DET ejpam-6732 21 34 measurable measurable ADJ ejpam-6732 21 35 functions function NOUN ejpam-6732 21 36 f f PRON ejpam-6732 21 37 defined define VERB ejpam-6732 21 38 on on ADP ejpam-6732 21 39 e e NOUN ejpam-6732 21 40 , , PUNCT ejpam-6732 21 41 such such ADJ ejpam-6732 21 42 that that SCONJ ejpam-6732 21 43 , , PUNCT ejpam-6732 21 44 for for ADP ejpam-6732 21 45 a a DET ejpam-6732 21 46 certain certain ADJ ejpam-6732 21 47 η η PROPN ejpam-6732 21 48 > > X ejpam-6732 21 49 0 0 PROPN ejpam-6732 21 50 , , PUNCT ejpam-6732 21 51 ∫ ∫ PROPN ejpam-6732 21 52 e e X ejpam-6732 21 53 ( ( PUNCT ejpam-6732 21 54 |f(x)| |f(x)| PROPN ejpam-6732 21 55 η η PROPN ejpam-6732 21 56 ) ) PUNCT ejpam-6732 21 57 p(y p(y PROPN ejpam-6732 21 58 ) ) PUNCT ejpam-6732 21 59 dy dy NOUN ejpam-6732 21 60 < < X ejpam-6732 21 61 ∞. ∞. PROPN ejpam-6732 21 62 its its PRON ejpam-6732 21 63 norm norm NOUN ejpam-6732 21 64 is be AUX ejpam-6732 21 65 given give VERB ejpam-6732 21 66 as as ADP ejpam-6732 21 67 ∥f∥lp(·)(e ∥f∥lp(·)(e ADJ ejpam-6732 21 68 ) ) PUNCT ejpam-6732 21 69 = = SYM ejpam-6732 21 70 inf inf NOUN ejpam-6732 21 71 { { PUNCT ejpam-6732 21 72 η η PROPN ejpam-6732 21 73 > > X ejpam-6732 21 74 0 0 NUM ejpam-6732 21 75 : : PUNCT ejpam-6732 22 1 ∫ ∫ PROPN ejpam-6732 22 2 e e X ejpam-6732 22 3 ( ( PUNCT ejpam-6732 22 4 |f(y)| |f(y)| PROPN ejpam-6732 22 5 η η PROPN ejpam-6732 22 6 ) ) PUNCT ejpam-6732 22 7 p(y p(y PROPN ejpam-6732 22 8 ) ) PUNCT ejpam-6732 22 9 dy dy VERB ejpam-6732 22 10 ≤ ≤ NUM ejpam-6732 22 11 1 1 NUM ejpam-6732 22 12 } } PUNCT ejpam-6732 22 13 . . PUNCT ejpam-6732 23 1 herz herz PROPN ejpam-6732 23 2 spaces space VERB ejpam-6732 23 3 with with ADP ejpam-6732 23 4 variable variable ADJ ejpam-6732 23 5 exponents exponent NOUN ejpam-6732 23 6 have have AUX ejpam-6732 23 7 emerged emerge VERB ejpam-6732 23 8 as as ADP ejpam-6732 23 9 a a DET ejpam-6732 23 10 generalization generalization NOUN ejpam-6732 23 11 of of ADP ejpam-6732 23 12 lebesgue lebesgue NOUN ejpam-6732 23 13 spaces space NOUN ejpam-6732 23 14 with with ADP ejpam-6732 23 15 variable variable ADJ ejpam-6732 23 16 exponents exponent NOUN ejpam-6732 23 17 . . PUNCT ejpam-6732 24 1 boundedness boundedness NOUN ejpam-6732 24 2 of of ADP ejpam-6732 24 3 sublinear sublinear NOUN ejpam-6732 24 4 operators operator NOUN ejpam-6732 24 5 on on ADP ejpam-6732 24 6 herz herz PROPN ejpam-6732 24 7 spaces space NOUN ejpam-6732 24 8 with with ADP ejpam-6732 24 9 variable variable ADJ ejpam-6732 24 10 exponents exponent NOUN ejpam-6732 24 11 , , PUNCT ejpam-6732 24 12 k̇α k̇α PROPN ejpam-6732 24 13 , , PUNCT ejpam-6732 24 14 q q NOUN ejpam-6732 24 15 p p X ejpam-6732 24 16 ( ( PUNCT ejpam-6732 24 17 · · PUNCT ejpam-6732 24 18 ) ) PUNCT ejpam-6732 24 19 and and CCONJ ejpam-6732 24 20 kα kα PROPN ejpam-6732 24 21 , , PUNCT ejpam-6732 24 22 q q PROPN ejpam-6732 24 23 p p X ejpam-6732 24 24 ( ( PUNCT ejpam-6732 24 25 · · PUNCT ejpam-6732 24 26 ) ) PUNCT ejpam-6732 24 27 , , PUNCT ejpam-6732 24 28 was be AUX ejpam-6732 24 29 shown show VERB ejpam-6732 24 30 by by ADP ejpam-6732 24 31 izuki izuki PROPN ejpam-6732 24 32 in in ADP ejpam-6732 24 33 [ [ X ejpam-6732 24 34 1 1 X ejpam-6732 24 35 ] ] PUNCT ejpam-6732 24 36 in in ADP ejpam-6732 24 37 2010 2010 NUM ejpam-6732 24 38 . . PUNCT ejpam-6732 25 1 boundedness boundedness NOUN ejpam-6732 25 2 results result NOUN ejpam-6732 25 3 for for ADP ejpam-6732 25 4 a a DET ejpam-6732 25 5 wide wide ADJ ejpam-6732 25 6 class class NOUN ejpam-6732 25 7 of of ADP ejpam-6732 25 8 classical classical ADJ ejpam-6732 25 9 operators operator NOUN ejpam-6732 25 10 on on ADP ejpam-6732 25 11 herz herz PROPN ejpam-6732 25 12 spaces space NOUN ejpam-6732 25 13 were be AUX ejpam-6732 25 14 later later ADV ejpam-6732 25 15 developed develop VERB ejpam-6732 25 16 by by ADP ejpam-6732 25 17 almeida almeida PROPN ejpam-6732 25 18 and and CCONJ ejpam-6732 25 19 drihem drihem NOUN ejpam-6732 25 20 in in ADP ejpam-6732 25 21 2012 2012 NUM ejpam-6732 25 22 [ [ X ejpam-6732 25 23 2 2 NUM ejpam-6732 25 24 ] ] PUNCT ejpam-6732 25 25 . . PUNCT ejpam-6732 26 1 these these DET ejpam-6732 26 2 spaces space NOUN ejpam-6732 26 3 were be AUX ejpam-6732 26 4 represented represent VERB ejpam-6732 26 5 as as ADP ejpam-6732 26 6 k̇ k̇ PROPN ejpam-6732 26 7 α(·)q α(·)q ADP ejpam-6732 26 8 p p X ejpam-6732 26 9 ( ( PUNCT ejpam-6732 26 10 · · PUNCT ejpam-6732 26 11 ) ) PUNCT ejpam-6732 26 12 and and CCONJ ejpam-6732 26 13 k k PROPN ejpam-6732 26 14 α(·),q α(·),q NUM ejpam-6732 26 15 p p X ejpam-6732 26 16 ( ( PUNCT ejpam-6732 26 17 · · PUNCT ejpam-6732 26 18 ) ) PUNCT ejpam-6732 26 19 . . PUNCT ejpam-6732 27 1 grand grand ADJ ejpam-6732 27 2 variable variable ADJ ejpam-6732 27 3 herz herz PROPN ejpam-6732 27 4 spaces space NOUN ejpam-6732 27 5 are be AUX ejpam-6732 27 6 the the DET ejpam-6732 27 7 generalization generalization NOUN ejpam-6732 27 8 of of ADP ejpam-6732 27 9 herz herz PROPN ejpam-6732 27 10 spaces space NOUN ejpam-6732 27 11 , , PUNCT ejpam-6732 27 12 for for ADP ejpam-6732 27 13 boundedness boundedness NOUN ejpam-6732 27 14 results result NOUN ejpam-6732 27 15 in in ADP ejpam-6732 27 16 these these DET ejpam-6732 27 17 spaces space NOUN ejpam-6732 27 18 see see VERB ejpam-6732 27 19 [ [ X ejpam-6732 27 20 3–8 3–8 NUM ejpam-6732 27 21 ] ] X ejpam-6732 27 22 . . PUNCT ejpam-6732 28 1 for for ADP ejpam-6732 28 2 more more ADJ ejpam-6732 28 3 results result NOUN ejpam-6732 28 4 in in ADP ejpam-6732 28 5 variable variable ADJ ejpam-6732 28 6 exponent exponent NOUN ejpam-6732 28 7 function function NOUN ejpam-6732 28 8 spaces space NOUN ejpam-6732 28 9 see see VERB ejpam-6732 28 10 [ [ X ejpam-6732 28 11 9–27 9–27 X ejpam-6732 28 12 ] ] X ejpam-6732 28 13 . . PUNCT ejpam-6732 29 1 in in ADP ejpam-6732 29 2 [ [ X ejpam-6732 29 3 28 28 NUM ejpam-6732 29 4 ] ] PUNCT ejpam-6732 29 5 , , PUNCT ejpam-6732 29 6 the the DET ejpam-6732 29 7 authors author NOUN ejpam-6732 29 8 introduced introduce VERB ejpam-6732 29 9 herz herz PROPN ejpam-6732 29 10 - - PUNCT ejpam-6732 29 11 morrey morrey NOUN ejpam-6732 29 12 - - PUNCT ejpam-6732 29 13 hardy hardy ADJ ejpam-6732 29 14 spaces space NOUN ejpam-6732 29 15 with with ADP ejpam-6732 29 16 variable variable ADJ ejpam-6732 29 17 exponents exponent NOUN ejpam-6732 29 18 and and CCONJ ejpam-6732 29 19 established establish VERB ejpam-6732 29 20 the the DET ejpam-6732 29 21 characterization characterization NOUN ejpam-6732 29 22 of of ADP ejpam-6732 29 23 these these DET ejpam-6732 29 24 spaces space NOUN ejpam-6732 29 25 in in ADP ejpam-6732 29 26 terms term NOUN ejpam-6732 29 27 of of ADP ejpam-6732 29 28 atom atom NOUN ejpam-6732 29 29 . . PUNCT ejpam-6732 30 1 the the DET ejpam-6732 30 2 authors author NOUN ejpam-6732 30 3 were be AUX ejpam-6732 30 4 able able ADJ ejpam-6732 30 5 to to PART ejpam-6732 30 6 determine determine VERB ejpam-6732 30 7 the the DET ejpam-6732 30 8 boundedness boundedness NOUN ejpam-6732 30 9 of of ADP ejpam-6732 30 10 certain certain ADJ ejpam-6732 30 11 singular singular ADJ ejpam-6732 30 12 integral integral ADJ ejpam-6732 30 13 operators operator NOUN ejpam-6732 30 14 on on ADP ejpam-6732 30 15 these these DET ejpam-6732 30 16 spaces space NOUN ejpam-6732 30 17 by by ADP ejpam-6732 30 18 applying apply VERB ejpam-6732 30 19 the the DET ejpam-6732 30 20 characterization characterization NOUN ejpam-6732 30 21 . . PUNCT ejpam-6732 31 1 in in ADP ejpam-6732 31 2 this this DET ejpam-6732 31 3 paper paper NOUN ejpam-6732 31 4 , , PUNCT ejpam-6732 31 5 we we PRON ejpam-6732 31 6 define define VERB ejpam-6732 31 7 the the DET ejpam-6732 31 8 idea idea NOUN ejpam-6732 31 9 of of ADP ejpam-6732 31 10 variable variable ADJ ejpam-6732 31 11 herz herz PROPN ejpam-6732 31 12 - - PUNCT ejpam-6732 31 13 morrey morrey NOUN ejpam-6732 31 14 - - PUNCT ejpam-6732 31 15 hardy hardy ADJ ejpam-6732 31 16 spaces space NOUN ejpam-6732 31 17 and and CCONJ ejpam-6732 31 18 using use VERB ejpam-6732 31 19 the the DET ejpam-6732 31 20 characterization characterization NOUN ejpam-6732 31 21 we we PRON ejpam-6732 31 22 obtain obtain VERB ejpam-6732 31 23 boundedness boundedness NOUN ejpam-6732 31 24 results result NOUN ejpam-6732 31 25 for for ADP ejpam-6732 31 26 some some DET ejpam-6732 31 27 new new ADJ ejpam-6732 31 28 operator operator NOUN ejpam-6732 31 29 in in ADP ejpam-6732 31 30 these these DET ejpam-6732 31 31 spaces space NOUN ejpam-6732 31 32 . . PUNCT ejpam-6732 32 1 many many ADJ ejpam-6732 32 2 classical classical ADJ ejpam-6732 32 3 function function NOUN ejpam-6732 32 4 spaces space NOUN ejpam-6732 32 5 , , PUNCT ejpam-6732 32 6 alongside alongside ADP ejpam-6732 32 7 hardy hardy ADJ ejpam-6732 32 8 - - PUNCT ejpam-6732 32 9 type type NOUN ejpam-6732 32 10 spaces space NOUN ejpam-6732 32 11 linked link VERB ejpam-6732 32 12 with with ADP ejpam-6732 32 13 operators operator NOUN ejpam-6732 32 14 , , PUNCT ejpam-6732 32 15 exhibit exhibit VERB ejpam-6732 32 16 atomic atomic ADJ ejpam-6732 32 17 and and CCONJ ejpam-6732 32 18 molecular molecular ADJ ejpam-6732 32 19 decompositions decomposition NOUN ejpam-6732 32 20 . . PUNCT ejpam-6732 33 1 these these DET ejpam-6732 33 2 decompositions decomposition NOUN ejpam-6732 33 3 simplify simplify VERB ejpam-6732 33 4 the the DET ejpam-6732 33 5 action action NOUN ejpam-6732 33 6 of of ADP ejpam-6732 33 7 linear linear PROPN ejpam-6732 33 8 operators operator NOUN ejpam-6732 33 9 on on ADP ejpam-6732 33 10 these these DET ejpam-6732 33 11 spaces space NOUN ejpam-6732 33 12 significantly significantly ADV ejpam-6732 33 13 ; ; PUNCT ejpam-6732 33 14 see see VERB ejpam-6732 33 15 [ [ X ejpam-6732 33 16 29–31 29–31 NOUN ejpam-6732 33 17 ] ] PUNCT ejpam-6732 33 18 . . PUNCT ejpam-6732 34 1 let let VERB ejpam-6732 34 2 sn−1 sn−1 PROPN ejpam-6732 34 3 is be AUX ejpam-6732 34 4 denoting denote VERB ejpam-6732 34 5 the the DET ejpam-6732 34 6 unit unit NOUN ejpam-6732 34 7 sphere sphere ADV ejpam-6732 34 8 in in ADP ejpam-6732 34 9 rn rn PROPN ejpam-6732 34 10 ( ( PUNCT ejpam-6732 34 11 n n CCONJ ejpam-6732 34 12 ≥ ≥ NOUN ejpam-6732 34 13 2 2 NUM ejpam-6732 34 14 ) ) PUNCT ejpam-6732 34 15 with with ADP ejpam-6732 34 16 the the DET ejpam-6732 34 17 normalized normalize VERB ejpam-6732 34 18 lebesgue lebesgue NOUN ejpam-6732 34 19 measure measure NOUN ejpam-6732 34 20 . . PUNCT ejpam-6732 35 1 let let VERB ejpam-6732 35 2 φ φ PROPN ejpam-6732 35 3 ∈ ∈ PROPN ejpam-6732 35 4 lr(sn−1 lr(sn−1 X ejpam-6732 35 5 ) ) PUNCT ejpam-6732 35 6 be be VERB ejpam-6732 35 7 a a DET ejpam-6732 35 8 homogeneous homogeneous ADJ ejpam-6732 35 9 function function NOUN ejpam-6732 35 10 of of ADP ejpam-6732 35 11 degree degree NOUN ejpam-6732 35 12 zero zero NUM ejpam-6732 35 13 such such ADJ ejpam-6732 35 14 that∫ that∫ NOUN ejpam-6732 35 15 sn−1 sn−1 PROPN ejpam-6732 35 16 φ(y′)dφ(y′ φ(y′)dφ(y′ PROPN ejpam-6732 35 17 ) ) PUNCT ejpam-6732 35 18 = = SYM ejpam-6732 35 19 0 0 NUM ejpam-6732 35 20 , , PUNCT ejpam-6732 35 21 ( ( PUNCT ejpam-6732 35 22 1.2 1.2 NUM ejpam-6732 35 23 ) ) PUNCT ejpam-6732 35 24 where where SCONJ ejpam-6732 35 25 y′ y′ NOUN ejpam-6732 35 26 = = SYM ejpam-6732 35 27 y/|y| y/|y| PROPN ejpam-6732 35 28 and and CCONJ ejpam-6732 35 29 y y PROPN ejpam-6732 35 30 is be AUX ejpam-6732 35 31 not not PART ejpam-6732 35 32 zero zero NUM ejpam-6732 35 33 . . PUNCT ejpam-6732 36 1 the the DET ejpam-6732 36 2 marcinkiewicz marcinkiewicz ADJ ejpam-6732 36 3 integral integral NOUN ejpam-6732 36 4 is be AUX ejpam-6732 36 5 define define VERB ejpam-6732 36 6 as as ADP ejpam-6732 36 7 µφ(g)(z1 µφ(g)(z1 ADJ ejpam-6732 36 8 ) ) PUNCT ejpam-6732 36 9 = = SYM ejpam-6732 37 1   PROPN ejpam-6732 37 2 ∞∫ ∞∫ PROPN ejpam-6732 37 3 0 0 PUNCT ejpam-6732 38 1 |rφ |rφ NUM ejpam-6732 38 2 , , PUNCT ejpam-6732 38 3 s(g)(z1)|2 s(g)(z1)|2 PRON ejpam-6732 38 4 ds ds PROPN ejpam-6732 38 5 s3 s3 NOUN ejpam-6732 38 6   PROPN ejpam-6732 38 7 1 1 NUM ejpam-6732 38 8 2 2 NUM ejpam-6732 38 9 , , PUNCT ejpam-6732 38 10 where where SCONJ ejpam-6732 38 11 rφ rφ VERB ejpam-6732 38 12 , , PUNCT ejpam-6732 38 13 s(g)(z1 s(g)(z1 ADJ ejpam-6732 38 14 ) ) PUNCT ejpam-6732 38 15 = = SYM ejpam-6732 39 1 ∫ ∫ PROPN ejpam-6732 39 2 |z1−z2|≤s |z1−z2|≤s PROPN ejpam-6732 39 3 φ(z1 φ(z1 ADJ ejpam-6732 39 4 − − PROPN ejpam-6732 39 5 z2 z2 PROPN ejpam-6732 39 6 ) ) PUNCT ejpam-6732 39 7 |z1 |z1 PROPN ejpam-6732 39 8 − − PROPN ejpam-6732 39 9 z2|n−β(z1)−1 z2|n−β(z1)−1 PROPN ejpam-6732 39 10 g(z2)dz2 g(z2)dz2 PROPN ejpam-6732 39 11 . . PUNCT ejpam-6732 40 1 b. b. PROPN ejpam-6732 40 2 sultan sultan PROPN ejpam-6732 40 3 et et PROPN ejpam-6732 40 4 al al PROPN ejpam-6732 40 5 . . PUNCT ejpam-6732 40 6 / / SYM ejpam-6732 40 7 eur eur PROPN ejpam-6732 40 8 . . PUNCT ejpam-6732 41 1 j. j. PROPN ejpam-6732 41 2 pure pure PROPN ejpam-6732 41 3 appl appl PROPN ejpam-6732 41 4 . . PROPN ejpam-6732 41 5 math math PROPN ejpam-6732 41 6 , , PUNCT ejpam-6732 41 7 18 18 NUM ejpam-6732 41 8 ( ( PUNCT ejpam-6732 41 9 4 4 NUM ejpam-6732 41 10 ) ) PUNCT ejpam-6732 41 11 ( ( PUNCT ejpam-6732 41 12 2025 2025 NUM ejpam-6732 41 13 ) ) PUNCT ejpam-6732 41 14 , , PUNCT ejpam-6732 41 15 6732 6732 NUM ejpam-6732 41 16 3 3 NUM ejpam-6732 41 17 of of ADP ejpam-6732 41 18 20 20 NUM ejpam-6732 41 19 let let VERB ejpam-6732 41 20 h h NOUN ejpam-6732 41 21 ∈ ∈ PROPN ejpam-6732 41 22 bmo bmo PROPN ejpam-6732 41 23 ( ( PUNCT ejpam-6732 41 24 rn rn PROPN ejpam-6732 41 25 ) ) PUNCT ejpam-6732 41 26 , , PUNCT ejpam-6732 41 27 then then ADV ejpam-6732 41 28 the the DET ejpam-6732 41 29 commutators commutator NOUN ejpam-6732 41 30 on on ADP ejpam-6732 41 31 variable variable ADJ ejpam-6732 41 32 marcinkiewicz marcinkiewicz ADJ ejpam-6732 41 33 fractional fractional ADJ ejpam-6732 41 34 integral integral ADJ ejpam-6732 41 35 operator operator NOUN ejpam-6732 41 36 are be AUX ejpam-6732 41 37 given give VERB ejpam-6732 41 38 as as ADP ejpam-6732 41 39 [ [ X ejpam-6732 41 40 h h X ejpam-6732 41 41 , , PUNCT ejpam-6732 41 42 µφ µφ ADP ejpam-6732 41 43 ] ] X ejpam-6732 41 44 m m VERB ejpam-6732 41 45 β β X ejpam-6732 41 46 ( ( PUNCT ejpam-6732 41 47 g)(z1 g)(z1 NOUN ejpam-6732 41 48 ) ) PUNCT ejpam-6732 41 49 = = SYM ejpam-6732 42 1   NUM ejpam-6732 42 2 ∞∫ ∞∫ PROPN ejpam-6732 42 3 0 0 NUM ejpam-6732 43 1 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ PROPN ejpam-6732 43 2 ∫ ∫ PROPN ejpam-6732 43 3 |z1−z2|≤s |z1−z2|≤s PROPN ejpam-6732 43 4 φ(z1 φ(z1 ADJ ejpam-6732 43 5 − − PROPN ejpam-6732 43 6 z2)[h(z1)− z2)[h(z1)− PROPN ejpam-6732 43 7 h(z2 h(z2 NOUN ejpam-6732 43 8 ) ) PUNCT ejpam-6732 43 9 ] ] PUNCT ejpam-6732 44 1 m m VERB ejpam-6732 44 2 |z1 |z1 NOUN ejpam-6732 44 3 − − PROPN ejpam-6732 44 4 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 44 5 ) ) PUNCT ejpam-6732 44 6 g(z2)dz2 g(z2)dz2 NOUN ejpam-6732 44 7 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ NOUN ejpam-6732 44 8 2 2 NUM ejpam-6732 44 9 ds ds NOUN ejpam-6732 44 10 s3 s3 NOUN ejpam-6732 44 11   PROPN ejpam-6732 44 12 1 1 NUM ejpam-6732 44 13 2 2 NUM ejpam-6732 44 14 . . PUNCT ejpam-6732 44 15 assume assume VERB ejpam-6732 44 16 g g PROPN ejpam-6732 44 17 ∈ ∈ PROPN ejpam-6732 44 18 l1 l1 PROPN ejpam-6732 44 19 loc(rn loc(rn PROPN ejpam-6732 44 20 ) ) PUNCT ejpam-6732 44 21 , , PUNCT ejpam-6732 44 22 the the DET ejpam-6732 44 23 definition definition NOUN ejpam-6732 44 24 of of ADP ejpam-6732 44 25 the the DET ejpam-6732 44 26 hardy hardy ADJ ejpam-6732 44 27 - - PUNCT ejpam-6732 44 28 littlewood littlewood NOUN ejpam-6732 44 29 maximal maximal ADJ ejpam-6732 44 30 operator operator NOUN ejpam-6732 44 31 is be AUX ejpam-6732 44 32 expressed express VERB ejpam-6732 44 33 as as ADP ejpam-6732 44 34 mg(z1 mg(z1 NOUN ejpam-6732 44 35 ) ) PUNCT ejpam-6732 44 36 = = SYM ejpam-6732 44 37 sup sup NOUN ejpam-6732 44 38 r>0 r>0 PROPN ejpam-6732 44 39 1 1 NUM ejpam-6732 44 40 |br(z1)| |br(z1)| PROPN ejpam-6732 44 41 ∫ ∫ PROPN ejpam-6732 44 42 br(z1 br(z1 NOUN ejpam-6732 44 43 ) ) PUNCT ejpam-6732 44 44 ∣∣g(z2)∣∣ ∣∣g(z2)∣∣ ADP ejpam-6732 44 45 dz2 dz2 NOUN ejpam-6732 44 46 , , PUNCT ejpam-6732 44 47 where where SCONJ ejpam-6732 44 48 br(z1 br(z1 NOUN ejpam-6732 44 49 ) ) PUNCT ejpam-6732 44 50 = = SYM ejpam-6732 44 51 { { PUNCT ejpam-6732 44 52 z2 z2 PROPN ejpam-6732 44 53 ∈ ∈ PROPN ejpam-6732 44 54 rn rn PROPN ejpam-6732 44 55 : : PUNCT ejpam-6732 45 1 |z1 |z1 PRON ejpam-6732 45 2 − − PROPN ejpam-6732 45 3 z2| z2| X ejpam-6732 45 4 < < X ejpam-6732 45 5 r r X ejpam-6732 45 6 } } PUNCT ejpam-6732 45 7 . . PUNCT ejpam-6732 46 1 the the DET ejpam-6732 46 2 set set NOUN ejpam-6732 46 3 b(rn b(rn NOUN ejpam-6732 46 4 ) ) PUNCT ejpam-6732 46 5 is be AUX ejpam-6732 46 6 comprised comprise VERB ejpam-6732 46 7 of of ADP ejpam-6732 46 8 p p X ejpam-6732 46 9 ( ( PUNCT ejpam-6732 46 10 · · PUNCT ejpam-6732 46 11 ) ) PUNCT ejpam-6732 46 12 ∈ ∈ PROPN ejpam-6732 46 13 p(rn p(rn PROPN ejpam-6732 46 14 ) ) PUNCT ejpam-6732 46 15 that that PRON ejpam-6732 46 16 fulfill fulfill VERB ejpam-6732 46 17 the the DET ejpam-6732 46 18 requirement requirement NOUN ejpam-6732 46 19 that that SCONJ ejpam-6732 46 20 m m PROPN ejpam-6732 46 21 is be AUX ejpam-6732 46 22 bounded bound VERB ejpam-6732 46 23 on on ADP ejpam-6732 46 24 lp(·)(rn lp(·)(rn PROPN ejpam-6732 46 25 ) ) PUNCT ejpam-6732 46 26 . . PUNCT ejpam-6732 47 1 now now ADV ejpam-6732 47 2 we we PRON ejpam-6732 47 3 will will AUX ejpam-6732 47 4 define define VERB ejpam-6732 47 5 the the DET ejpam-6732 47 6 well well ADV ejpam-6732 47 7 known know VERB ejpam-6732 47 8 log log NOUN ejpam-6732 47 9 - - PUNCT ejpam-6732 47 10 condition condition NOUN ejpam-6732 47 11 |p(h1)− |p(h1)− VERB ejpam-6732 47 12 p(h2)| p(h2)| PROPN ejpam-6732 47 13 ≤ ≤ ADJ ejpam-6732 47 14 c(p c(p NOUN ejpam-6732 47 15 ) ) PUNCT ejpam-6732 48 1 − − PROPN ejpam-6732 49 1 ln ln NOUN ejpam-6732 49 2 |h1 |h1 PUNCT ejpam-6732 49 3 − − PROPN ejpam-6732 50 1 h2| h2| INTJ ejpam-6732 50 2 , , PUNCT ejpam-6732 50 3 |h1 |h1 NUM ejpam-6732 50 4 − − PROPN ejpam-6732 51 1 h2| h2| PROPN ejpam-6732 51 2 ≤ ≤ NUM ejpam-6732 51 3 1 1 NUM ejpam-6732 51 4 2 2 NUM ejpam-6732 51 5 , , PUNCT ejpam-6732 51 6 h1 h1 PROPN ejpam-6732 51 7 , , PUNCT ejpam-6732 51 8 h2 h2 PROPN ejpam-6732 51 9 ∈ ∈ PROPN ejpam-6732 51 10 e e PROPN ejpam-6732 51 11 , , PUNCT ejpam-6732 51 12 ( ( PUNCT ejpam-6732 51 13 1.3 1.3 NUM ejpam-6732 51 14 ) ) PUNCT ejpam-6732 51 15 where where SCONJ ejpam-6732 51 16 c(p c(p NOUN ejpam-6732 51 17 ) ) PUNCT ejpam-6732 51 18 > > X ejpam-6732 52 1 0 0 X ejpam-6732 52 2 . . PUNCT ejpam-6732 53 1 and and CCONJ ejpam-6732 53 2 the the DET ejpam-6732 53 3 decay decay NOUN ejpam-6732 53 4 condition condition NOUN ejpam-6732 53 5 : : PUNCT ejpam-6732 53 6 there there PRON ejpam-6732 53 7 exists exist VERB ejpam-6732 53 8 a a DET ejpam-6732 53 9 number number NOUN ejpam-6732 53 10 p∞ p∞ NOUN ejpam-6732 53 11 ∈ ∈ PROPN ejpam-6732 53 12 ( ( PUNCT ejpam-6732 53 13 1,∞ 1,∞ NUM ejpam-6732 53 14 ) ) PUNCT ejpam-6732 53 15 , , PUNCT ejpam-6732 53 16 such such ADJ ejpam-6732 53 17 that that PRON ejpam-6732 53 18 |p(h)− |p(h)− ADJ ejpam-6732 53 19 p∞| p∞| NOUN ejpam-6732 53 20 ≤ ≤ NUM ejpam-6732 53 21 c c PROPN ejpam-6732 53 22 ln(e+ ln(e+ PROPN ejpam-6732 53 23 |h| |h| PROPN ejpam-6732 53 24 ) ) PUNCT ejpam-6732 53 25 , , PUNCT ejpam-6732 53 26 ( ( PUNCT ejpam-6732 53 27 1.4 1.4 NUM ejpam-6732 53 28 ) ) PUNCT ejpam-6732 53 29 and and CCONJ ejpam-6732 53 30 also also ADV ejpam-6732 53 31 decay decay VERB ejpam-6732 53 32 condition condition NOUN ejpam-6732 53 33 |p(h)− |p(h)− VERB ejpam-6732 53 34 p0| p0| ADJ ejpam-6732 53 35 ≤ ≤ PUNCT ejpam-6732 53 36 c c PROPN ejpam-6732 53 37 ln ln PROPN ejpam-6732 53 38 |h| |h| PROPN ejpam-6732 53 39 , , PUNCT ejpam-6732 53 40 |h| |h| PROPN ejpam-6732 53 41 ≤ ≤ PROPN ejpam-6732 53 42 1 1 NUM ejpam-6732 53 43 2 2 NUM ejpam-6732 53 44 , , PUNCT ejpam-6732 53 45 ( ( PUNCT ejpam-6732 53 46 1.5 1.5 NUM ejpam-6732 53 47 ) ) PUNCT ejpam-6732 53 48 holds hold VERB ejpam-6732 53 49 for for ADP ejpam-6732 53 50 some some DET ejpam-6732 53 51 p0 p0 NOUN ejpam-6732 53 52 ∈ ∈ NOUN ejpam-6732 53 53 ( ( PUNCT ejpam-6732 53 54 1,∞ 1,∞ NUM ejpam-6732 53 55 ) ) PUNCT ejpam-6732 53 56 . . PUNCT ejpam-6732 54 1 we we PRON ejpam-6732 54 2 use use VERB ejpam-6732 54 3 these these DET ejpam-6732 54 4 notations notation NOUN ejpam-6732 54 5 in in ADP ejpam-6732 54 6 this this DET ejpam-6732 54 7 article article NOUN ejpam-6732 54 8 : : PUNCT ejpam-6732 54 9 ( ( PUNCT ejpam-6732 54 10 i i NOUN ejpam-6732 54 11 ) ) PUNCT ejpam-6732 54 12 the the DET ejpam-6732 54 13 set set NOUN ejpam-6732 54 14 p(e p(e NOUN ejpam-6732 54 15 ) ) PUNCT ejpam-6732 54 16 consists consist VERB ejpam-6732 54 17 of of ADP ejpam-6732 54 18 all all DET ejpam-6732 54 19 measurable measurable ADJ ejpam-6732 54 20 functions function NOUN ejpam-6732 54 21 p p X ejpam-6732 54 22 ( ( PUNCT ejpam-6732 54 23 · · PUNCT ejpam-6732 54 24 ) ) PUNCT ejpam-6732 54 25 satisfying satisfy VERB ejpam-6732 54 26 p− p− PROPN ejpam-6732 54 27 > > SYM ejpam-6732 54 28 1 1 NUM ejpam-6732 54 29 and and CCONJ ejpam-6732 54 30 p+ p+ X ejpam-6732 54 31 < < X ejpam-6732 54 32 ∞. ∞. PROPN ejpam-6732 54 33 ( ( PUNCT ejpam-6732 54 34 ii ii NOUN ejpam-6732 54 35 ) ) PUNCT ejpam-6732 54 36 p p NOUN ejpam-6732 54 37 log log NOUN ejpam-6732 54 38 = = PUNCT ejpam-6732 54 39 p p PROPN ejpam-6732 54 40 log(e log(e PROPN ejpam-6732 54 41 ) ) PUNCT ejpam-6732 54 42 consists consist VERB ejpam-6732 54 43 of of ADP ejpam-6732 54 44 all all DET ejpam-6732 54 45 functions function NOUN ejpam-6732 54 46 p p X ejpam-6732 54 47 ∈ ∈ PROPN ejpam-6732 54 48 p(e p(e NOUN ejpam-6732 54 49 ) ) PUNCT ejpam-6732 55 1 satisfying satisfy VERB ejpam-6732 55 2 ( ( PUNCT ejpam-6732 55 3 1.1 1.1 NUM ejpam-6732 55 4 ) ) PUNCT ejpam-6732 55 5 and and CCONJ ejpam-6732 55 6 ( ( PUNCT ejpam-6732 55 7 1.3 1.3 NUM ejpam-6732 55 8 ) ) PUNCT ejpam-6732 55 9 . . PUNCT ejpam-6732 56 1 ( ( PUNCT ejpam-6732 56 2 iii iii X ejpam-6732 56 3 ) ) PUNCT ejpam-6732 56 4 p∞(e p∞(e PROPN ejpam-6732 56 5 ) ) PUNCT ejpam-6732 56 6 and and CCONJ ejpam-6732 56 7 p0,∞(e p0,∞(e NOUN ejpam-6732 56 8 ) ) PUNCT ejpam-6732 56 9 are be AUX ejpam-6732 56 10 the the DET ejpam-6732 56 11 subsets subset NOUN ejpam-6732 56 12 of of ADP ejpam-6732 56 13 p(e p(e NOUN ejpam-6732 56 14 ) ) PUNCT ejpam-6732 56 15 and and CCONJ ejpam-6732 56 16 values value NOUN ejpam-6732 56 17 of of ADP ejpam-6732 56 18 these these DET ejpam-6732 56 19 subsets subset NOUN ejpam-6732 56 20 lies lie VERB ejpam-6732 56 21 in in ADP ejpam-6732 56 22 [ [ X ejpam-6732 56 23 1,∞ 1,∞ NUM ejpam-6732 56 24 ) ) PUNCT ejpam-6732 56 25 which which PRON ejpam-6732 56 26 satisfy satisfy VERB ejpam-6732 56 27 the the DET ejpam-6732 56 28 condition condition NOUN ejpam-6732 56 29 ( ( PUNCT ejpam-6732 56 30 1.4 1.4 NUM ejpam-6732 56 31 ) ) PUNCT ejpam-6732 56 32 and and CCONJ ejpam-6732 56 33 both both DET ejpam-6732 56 34 conditions condition NOUN ejpam-6732 56 35 ( ( PUNCT ejpam-6732 56 36 1.4 1.4 NUM ejpam-6732 56 37 ) ) PUNCT ejpam-6732 56 38 and and CCONJ ejpam-6732 56 39 ( ( PUNCT ejpam-6732 56 40 1.5 1.5 NUM ejpam-6732 56 41 ) ) PUNCT ejpam-6732 56 42 respectively respectively ADV ejpam-6732 56 43 . . PUNCT ejpam-6732 57 1 ( ( PUNCT ejpam-6732 57 2 iv iv X ejpam-6732 57 3 ) ) PUNCT ejpam-6732 57 4 χi χi NOUN ejpam-6732 57 5 = = SYM ejpam-6732 57 6 χfi χfi NOUN ejpam-6732 57 7 , , PUNCT ejpam-6732 57 8 fi fi NOUN ejpam-6732 57 9 = = NOUN ejpam-6732 57 10 bi bi PROPN ejpam-6732 57 11 \bi−1 \bi−1 PROPN ejpam-6732 57 12 , , PUNCT ejpam-6732 57 13 bi bi NOUN ejpam-6732 57 14 = = SYM ejpam-6732 57 15 b(0 b(0 PROPN ejpam-6732 57 16 , , PUNCT ejpam-6732 57 17 2i 2i NUM ejpam-6732 57 18 ) ) PUNCT ejpam-6732 57 19 = = PRON ejpam-6732 58 1 { { PUNCT ejpam-6732 58 2 x x PUNCT ejpam-6732 58 3 ∈ ∈ PROPN ejpam-6732 58 4 rn rn NOUN ejpam-6732 58 5 : : PUNCT ejpam-6732 58 6 |x| |x| PROPN ejpam-6732 58 7 < < X ejpam-6732 58 8 2i 2i NUM ejpam-6732 58 9 } } PUNCT ejpam-6732 58 10 for for ADP ejpam-6732 58 11 all all PRON ejpam-6732 59 1 i i PRON ejpam-6732 59 2 ∈ ∈ PROPN ejpam-6732 59 3 z. z. PROPN ejpam-6732 59 4 ( ( PUNCT ejpam-6732 59 5 v v NOUN ejpam-6732 59 6 ) ) PUNCT ejpam-6732 59 7 let let VERB ejpam-6732 59 8 e e PRON ejpam-6732 59 9 be be AUX ejpam-6732 59 10 a a DET ejpam-6732 59 11 measurable measurable ADJ ejpam-6732 59 12 subset subset NOUN ejpam-6732 59 13 in in ADP ejpam-6732 59 14 rn rn PROPN ejpam-6732 59 15 , , PUNCT ejpam-6732 59 16 then then ADV ejpam-6732 59 17 |e| |e| DET ejpam-6732 59 18 denotes denote VERB ejpam-6732 59 19 the the DET ejpam-6732 59 20 lebesgue lebesgue ADJ ejpam-6732 59 21 measure measure NOUN ejpam-6732 59 22 and and CCONJ ejpam-6732 59 23 χe χe PROPN ejpam-6732 59 24 is be AUX ejpam-6732 59 25 the the DET ejpam-6732 59 26 characteristic characteristic ADJ ejpam-6732 59 27 function function NOUN ejpam-6732 59 28 . . PUNCT ejpam-6732 60 1 b. b. PROPN ejpam-6732 60 2 sultan sultan PROPN ejpam-6732 60 3 et et PROPN ejpam-6732 60 4 al al PROPN ejpam-6732 60 5 . . PUNCT ejpam-6732 60 6 / / SYM ejpam-6732 60 7 eur eur PROPN ejpam-6732 60 8 . . PUNCT ejpam-6732 61 1 j. j. PROPN ejpam-6732 61 2 pure pure PROPN ejpam-6732 61 3 appl appl PROPN ejpam-6732 61 4 . . PROPN ejpam-6732 61 5 math math PROPN ejpam-6732 61 6 , , PUNCT ejpam-6732 61 7 18 18 NUM ejpam-6732 61 8 ( ( PUNCT ejpam-6732 61 9 4 4 NUM ejpam-6732 61 10 ) ) PUNCT ejpam-6732 61 11 ( ( PUNCT ejpam-6732 61 12 2025 2025 NUM ejpam-6732 61 13 ) ) PUNCT ejpam-6732 61 14 , , PUNCT ejpam-6732 61 15 6732 6732 NUM ejpam-6732 61 16 4 4 NUM ejpam-6732 61 17 of of ADP ejpam-6732 61 18 20 20 NUM ejpam-6732 61 19 ( ( PUNCT ejpam-6732 61 20 vi vi NOUN ejpam-6732 61 21 ) ) PUNCT ejpam-6732 61 22 let let VERB ejpam-6732 61 23 β β X ejpam-6732 61 24 = = SYM ejpam-6732 61 25 ( ( PUNCT ejpam-6732 61 26 β1 β1 PROPN ejpam-6732 61 27 , , PUNCT ejpam-6732 61 28 β2 β2 VERB ejpam-6732 61 29 , , PUNCT ejpam-6732 61 30 · · PUNCT ejpam-6732 61 31 · · PUNCT ejpam-6732 61 32 · · PUNCT ejpam-6732 61 33 , , PUNCT ejpam-6732 61 34 βn βn PROPN ejpam-6732 61 35 ) ) PUNCT ejpam-6732 61 36 then then ADV ejpam-6732 61 37 |β| |β| PROPN ejpam-6732 61 38 is be AUX ejpam-6732 61 39 defined define VERB ejpam-6732 61 40 as as ADP ejpam-6732 61 41 |β| |β| NOUN ejpam-6732 61 42 = = SYM ejpam-6732 61 43 β1 β1 PROPN ejpam-6732 61 44 , , PUNCT ejpam-6732 61 45 β2 β2 NOUN ejpam-6732 61 46 + + NOUN ejpam-6732 61 47 · · PUNCT ejpam-6732 61 48 · · PUNCT ejpam-6732 61 49 · · PUNCT ejpam-6732 62 1 + + CCONJ ejpam-6732 62 2 βn βn ADJ ejpam-6732 62 3 . . PUNCT ejpam-6732 62 4 ( ( PUNCT ejpam-6732 62 5 vii vii PROPN ejpam-6732 62 6 ) ) PUNCT ejpam-6732 62 7 the the DET ejpam-6732 62 8 symbol symbol NOUN ejpam-6732 62 9 n0 n0 PROPN ejpam-6732 62 10 denotes denote VERB ejpam-6732 62 11 the the DET ejpam-6732 62 12 set set NOUN ejpam-6732 62 13 of of ADP ejpam-6732 62 14 all all DET ejpam-6732 62 15 nonnegative nonnegative ADJ ejpam-6732 62 16 integers integer NOUN ejpam-6732 62 17 . . PUNCT ejpam-6732 63 1 for for ADP ejpam-6732 63 2 m m PROPN ejpam-6732 63 3 ∈ ∈ PROPN ejpam-6732 63 4 n0 n0 NUM ejpam-6732 63 5 , , PUNCT ejpam-6732 63 6 we we PRON ejpam-6732 63 7 denote denote VERB ejpam-6732 63 8 χ̃m χ̃m PROPN ejpam-6732 63 9 : : PUNCT ejpam-6732 63 10 = = SYM ejpam-6732 63 11 χfm χfm NOUN ejpam-6732 63 12 if if SCONJ ejpam-6732 63 13 m m PROPN ejpam-6732 63 14 ≥ ≥ VERB ejpam-6732 63 15 1 1 NUM ejpam-6732 63 16 and and CCONJ ejpam-6732 63 17 χ̃0 χ̃0 NOUN ejpam-6732 63 18 : : PUNCT ejpam-6732 63 19 = = SYM ejpam-6732 63 20 χb0 χb0 ADJ ejpam-6732 63 21 . . PUNCT ejpam-6732 64 1 ( ( PUNCT ejpam-6732 64 2 viii viii NOUN ejpam-6732 64 3 ) ) PUNCT ejpam-6732 64 4 c c NOUN ejpam-6732 64 5 is be AUX ejpam-6732 64 6 a a DET ejpam-6732 64 7 positive positive ADJ ejpam-6732 64 8 constant constant NOUN ejpam-6732 64 9 . . PUNCT ejpam-6732 65 1 ( ( PUNCT ejpam-6732 65 2 ix ix ADP ejpam-6732 65 3 ) ) PUNCT ejpam-6732 65 4 by by ADP ejpam-6732 65 5 a a DET ejpam-6732 65 6 ≲ ≲ PROPN ejpam-6732 65 7 b b PROPN ejpam-6732 65 8 , , PUNCT ejpam-6732 65 9 we we PRON ejpam-6732 65 10 mean mean VERB ejpam-6732 66 1 a a DET ejpam-6732 66 2 ≤ ≤ PROPN ejpam-6732 66 3 cb cb PROPN ejpam-6732 66 4 . . PUNCT ejpam-6732 67 1 lemma lemma PROPN ejpam-6732 68 1 1 1 NUM ejpam-6732 68 2 . . PUNCT ejpam-6732 69 1 [ [ X ejpam-6732 69 2 32 32 NUM ejpam-6732 69 3 ] ] PUNCT ejpam-6732 69 4 let let VERB ejpam-6732 69 5 d d PRON ejpam-6732 69 6 > > X ejpam-6732 69 7 1 1 NUM ejpam-6732 69 8 and and CCONJ ejpam-6732 69 9 p p NOUN ejpam-6732 69 10 ∈ ∈ PROPN ejpam-6732 69 11 p0,∞(rn p0,∞(rn NUM ejpam-6732 69 12 ) ) PUNCT ejpam-6732 69 13 . . PUNCT ejpam-6732 70 1 then then ADV ejpam-6732 70 2 1 1 NUM ejpam-6732 70 3 r0 r0 NOUN ejpam-6732 70 4 o o NOUN ejpam-6732 70 5 n n PRON ejpam-6732 70 6 p(0 p(0 NOUN ejpam-6732 70 7 ) ) PUNCT ejpam-6732 70 8 ≤ ≤ NOUN ejpam-6732 70 9 ∥χfo ∥χfo NOUN ejpam-6732 70 10 , , PUNCT ejpam-6732 70 11 do do VERB ejpam-6732 70 12 ∥p ∥p VERB ejpam-6732 70 13 ( ( PUNCT ejpam-6732 70 14 · · PUNCT ejpam-6732 70 15 ) ) PUNCT ejpam-6732 70 16 ≤ ≤ NOUN ejpam-6732 70 17 r0o r0o PROPN ejpam-6732 70 18 n n PRON ejpam-6732 70 19 p(0 p(0 PROPN ejpam-6732 70 20 ) ) PUNCT ejpam-6732 70 21 , , PUNCT ejpam-6732 70 22 for for ADP ejpam-6732 70 23 0 0 NUM ejpam-6732 70 24 < < X ejpam-6732 70 25 o o X ejpam-6732 70 26 ≤ ≤ NUM ejpam-6732 70 27 1 1 NUM ejpam-6732 70 28 ( ( PUNCT ejpam-6732 70 29 1.6 1.6 NUM ejpam-6732 70 30 ) ) PUNCT ejpam-6732 70 31 and and CCONJ ejpam-6732 70 32 1 1 NUM ejpam-6732 70 33 r∞ r∞ ADJ ejpam-6732 70 34 o o NOUN ejpam-6732 70 35 n n X ejpam-6732 70 36 p∞ p∞ PROPN ejpam-6732 70 37 ≤ ≤ NOUN ejpam-6732 70 38 ∥χfo ∥χfo NOUN ejpam-6732 70 39 , , PUNCT ejpam-6732 70 40 do do VERB ejpam-6732 70 41 ∥p ∥p VERB ejpam-6732 70 42 ( ( PUNCT ejpam-6732 70 43 · · PUNCT ejpam-6732 70 44 ) ) PUNCT ejpam-6732 70 45 ≤ ≤ NOUN ejpam-6732 70 46 r∞o r∞o PROPN ejpam-6732 70 47 n n PRON ejpam-6732 70 48 p∞ p∞ PROPN ejpam-6732 70 49 , , PUNCT ejpam-6732 70 50 for for ADP ejpam-6732 70 51 o o PROPN ejpam-6732 70 52 ≥ ≥ NUM ejpam-6732 70 53 1 1 NUM ejpam-6732 70 54 , , PUNCT ejpam-6732 70 55 ( ( PUNCT ejpam-6732 70 56 1.7 1.7 NUM ejpam-6732 70 57 ) ) PUNCT ejpam-6732 70 58 respectively respectively ADV ejpam-6732 70 59 , , PUNCT ejpam-6732 70 60 where where SCONJ ejpam-6732 70 61 r0 r0 NOUN ejpam-6732 70 62 ≥ ≥ NOUN ejpam-6732 70 63 1 1 NUM ejpam-6732 70 64 and and CCONJ ejpam-6732 70 65 r∞ r∞ PROPN ejpam-6732 70 66 ≥ ≥ NOUN ejpam-6732 70 67 1 1 NUM ejpam-6732 70 68 and and CCONJ ejpam-6732 70 69 depending depend VERB ejpam-6732 70 70 on on ADP ejpam-6732 70 71 d d PROPN ejpam-6732 70 72 but but CCONJ ejpam-6732 70 73 independent independent ADJ ejpam-6732 70 74 of of ADP ejpam-6732 70 75 o. o. PROPN ejpam-6732 70 76 lemma lemma PROPN ejpam-6732 70 77 2 2 NUM ejpam-6732 70 78 . . PUNCT ejpam-6732 71 1 [ [ X ejpam-6732 71 2 33 33 NUM ejpam-6732 71 3 ] ] PUNCT ejpam-6732 71 4 let let VERB ejpam-6732 71 5 p p X ejpam-6732 71 6 ( ( PUNCT ejpam-6732 71 7 · · PUNCT ejpam-6732 71 8 ) ) PUNCT ejpam-6732 71 9 be be AUX ejpam-6732 71 10 a a DET ejpam-6732 71 11 function function NOUN ejpam-6732 71 12 within within ADP ejpam-6732 71 13 the the DET ejpam-6732 71 14 class class NOUN ejpam-6732 71 15 b(rn b(rn NOUN ejpam-6732 71 16 ) ) PUNCT ejpam-6732 71 17 . . PUNCT ejpam-6732 72 1 for for ADP ejpam-6732 72 2 any any DET ejpam-6732 72 3 ball ball NOUN ejpam-6732 72 4 b b PROPN ejpam-6732 72 5 in in ADP ejpam-6732 72 6 rn rn PROPN ejpam-6732 72 7 , , PUNCT ejpam-6732 72 8 there there PRON ejpam-6732 72 9 exists exist VERB ejpam-6732 72 10 a a DET ejpam-6732 72 11 positive positive ADJ ejpam-6732 72 12 constant constant ADJ ejpam-6732 72 13 c c NOUN ejpam-6732 72 14 such such ADJ ejpam-6732 72 15 that that SCONJ ejpam-6732 72 16 the the DET ejpam-6732 72 17 inequality inequality NOUN ejpam-6732 72 18 1 1 NUM ejpam-6732 72 19 |b| |b| PROPN ejpam-6732 72 20 ∥χb∥p(·)∥χb∥p′ ∥χb∥p(·)∥χb∥p′ NOUN ejpam-6732 72 21 ( ( PUNCT ejpam-6732 72 22 · · PUNCT ejpam-6732 72 23 ) ) PUNCT ejpam-6732 72 24 ≤ ≤ NOUN ejpam-6732 72 25 c c X ejpam-6732 72 26 , , PUNCT ejpam-6732 72 27 holds hold VERB ejpam-6732 72 28 . . PUNCT ejpam-6732 73 1 lemma lemma PROPN ejpam-6732 73 2 3 3 NUM ejpam-6732 73 3 . . PUNCT ejpam-6732 74 1 [ [ X ejpam-6732 74 2 33 33 NUM ejpam-6732 74 3 ] ] PUNCT ejpam-6732 74 4 assuming assume VERB ejpam-6732 74 5 that that SCONJ ejpam-6732 74 6 p p X ejpam-6732 74 7 ( ( PUNCT ejpam-6732 74 8 · · PUNCT ejpam-6732 74 9 ) ) PUNCT ejpam-6732 74 10 is be AUX ejpam-6732 74 11 a a DET ejpam-6732 74 12 function function NOUN ejpam-6732 74 13 in in ADP ejpam-6732 74 14 the the DET ejpam-6732 74 15 class class NOUN ejpam-6732 74 16 b(rn b(rn NOUN ejpam-6732 74 17 ) ) PUNCT ejpam-6732 74 18 , , PUNCT ejpam-6732 74 19 there there PRON ejpam-6732 74 20 exists exist VERB ejpam-6732 74 21 a a DET ejpam-6732 74 22 positive positive ADJ ejpam-6732 74 23 constant constant ADJ ejpam-6732 74 24 c c NOUN ejpam-6732 74 25 such such ADJ ejpam-6732 74 26 that that PRON ejpam-6732 74 27 , , PUNCT ejpam-6732 74 28 for for ADP ejpam-6732 74 29 every every DET ejpam-6732 74 30 ball ball NOUN ejpam-6732 74 31 b b PROPN ejpam-6732 74 32 in in ADP ejpam-6732 74 33 rn rn PROPN ejpam-6732 74 34 and and CCONJ ejpam-6732 74 35 every every DET ejpam-6732 74 36 measurable measurable ADJ ejpam-6732 74 37 subset subset NOUN ejpam-6732 74 38 s s VERB ejpam-6732 74 39 within within ADP ejpam-6732 74 40 b b NOUN ejpam-6732 74 41 , , PUNCT ejpam-6732 74 42 the the DET ejpam-6732 74 43 following follow VERB ejpam-6732 74 44 inequalities inequality NOUN ejpam-6732 74 45 hold hold VERB ejpam-6732 74 46 : : PUNCT ejpam-6732 74 47 ∥χb∥p ∥χb∥p NOUN ejpam-6732 74 48 ( ( PUNCT ejpam-6732 74 49 · · PUNCT ejpam-6732 74 50 ) ) PUNCT ejpam-6732 74 51 ∥χs∥p ∥χs∥p PROPN ejpam-6732 74 52 ( ( PUNCT ejpam-6732 74 53 · · PUNCT ejpam-6732 74 54 ) ) PUNCT ejpam-6732 74 55 ≤ ≤ NOUN ejpam-6732 75 1 c c NOUN ejpam-6732 75 2 |b| |b| PROPN ejpam-6732 75 3 |s| |s| PROPN ejpam-6732 75 4 , , PUNCT ejpam-6732 75 5 ∥χs∥p ∥χs∥p PROPN ejpam-6732 75 6 ( ( PUNCT ejpam-6732 75 7 · · PUNCT ejpam-6732 75 8 ) ) PUNCT ejpam-6732 75 9 ∥χb∥p ∥χb∥p PROPN ejpam-6732 75 10 ( ( PUNCT ejpam-6732 75 11 · · PUNCT ejpam-6732 75 12 ) ) PUNCT ejpam-6732 75 13 ≤ ≤ NUM ejpam-6732 76 1 c c X ejpam-6732 76 2 ( ( PUNCT ejpam-6732 76 3 |s| |s| NOUN ejpam-6732 76 4 |b| |b| PROPN ejpam-6732 76 5 ) ) PUNCT ejpam-6732 76 6 δ1 δ1 NOUN ejpam-6732 76 7 , , PUNCT ejpam-6732 76 8 ∥χs∥p′ ∥χs∥p′ PROPN ejpam-6732 76 9 ( ( PUNCT ejpam-6732 76 10 · · PUNCT ejpam-6732 76 11 ) ) PUNCT ejpam-6732 76 12 ∥χb∥p′ ∥χb∥p′ PROPN ejpam-6732 76 13 ( ( PUNCT ejpam-6732 76 14 · · PUNCT ejpam-6732 76 15 ) ) PUNCT ejpam-6732 76 16 ≤ ≤ NUM ejpam-6732 77 1 c c X ejpam-6732 77 2 ( ( PUNCT ejpam-6732 77 3 |s| |s| NOUN ejpam-6732 77 4 |b| |b| PROPN ejpam-6732 77 5 ) ) PUNCT ejpam-6732 77 6 δ2 δ2 VERB ejpam-6732 77 7 , , PUNCT ejpam-6732 77 8 where where SCONJ ejpam-6732 77 9 δ1 δ1 NOUN ejpam-6732 77 10 and and CCONJ ejpam-6732 77 11 δ2 δ2 PROPN ejpam-6732 77 12 are be AUX ejpam-6732 77 13 constants constant NOUN ejpam-6732 77 14 satisfying satisfy VERB ejpam-6732 77 15 0 0 NUM ejpam-6732 77 16 < < X ejpam-6732 77 17 δ1 δ1 NOUN ejpam-6732 77 18 , , PUNCT ejpam-6732 77 19 δ2 δ2 VERB ejpam-6732 77 20 < < X ejpam-6732 77 21 1 1 NUM ejpam-6732 77 22 . . PUNCT ejpam-6732 78 1 lemma lemma PROPN ejpam-6732 78 2 4 4 X ejpam-6732 78 3 . . PUNCT ejpam-6732 79 1 [ [ X ejpam-6732 79 2 34 34 NUM ejpam-6732 79 3 ] ] PUNCT ejpam-6732 79 4 let let VERB ejpam-6732 79 5 f f PROPN ejpam-6732 79 6 ∈ ∈ PROPN ejpam-6732 79 7 lp(·)(e lp(·)(e PROPN ejpam-6732 79 8 ) ) PUNCT ejpam-6732 79 9 , , PUNCT ejpam-6732 79 10 g g PROPN ejpam-6732 79 11 ∈ ∈ PROPN ejpam-6732 79 12 lq(·)(e lq(·)(e PROPN ejpam-6732 79 13 ) ) PUNCT ejpam-6732 79 14 where where SCONJ ejpam-6732 79 15 e e PROPN ejpam-6732 79 16 ⊆ ⊆ NUM ejpam-6732 79 17 rn rn PROPN ejpam-6732 79 18 , , PUNCT ejpam-6732 79 19 and and CCONJ ejpam-6732 79 20 1 1 NUM ejpam-6732 79 21 ≤ ≤ NUM ejpam-6732 79 22 p−(e p−(e NOUN ejpam-6732 79 23 ) ) PUNCT ejpam-6732 79 24 ≤ ≤ NUM ejpam-6732 79 25 p+(e p+(e PROPN ejpam-6732 79 26 ) ) PUNCT ejpam-6732 80 1 ≤ ≤ NOUN ejpam-6732 80 2 ∞. ∞. PROPN ejpam-6732 80 3 then then ADV ejpam-6732 80 4 ∥fg∥r ∥fg∥r PROPN ejpam-6732 80 5 ( ( PUNCT ejpam-6732 80 6 · · PUNCT ejpam-6732 80 7 ) ) PUNCT ejpam-6732 81 1 ≤ ≤ PUNCT ejpam-6732 81 2 ∥f∥p(·)∥g∥q ∥f∥p(·)∥g∥q PROPN ejpam-6732 81 3 ( ( PUNCT ejpam-6732 81 4 · · PUNCT ejpam-6732 81 5 ) ) PUNCT ejpam-6732 81 6 where where SCONJ ejpam-6732 81 7 1 1 NUM ejpam-6732 81 8 r(z r(z NOUN ejpam-6732 81 9 ) ) PUNCT ejpam-6732 81 10 = = SYM ejpam-6732 81 11 1 1 NUM ejpam-6732 81 12 p(z p(z NOUN ejpam-6732 81 13 ) ) PUNCT ejpam-6732 81 14 + + CCONJ ejpam-6732 81 15 1 1 NUM ejpam-6732 81 16 q(z q(z PROPN ejpam-6732 81 17 ) ) PUNCT ejpam-6732 81 18 . . PUNCT ejpam-6732 82 1 definition definition NOUN ejpam-6732 82 2 5 5 NUM ejpam-6732 82 3 ( ( PUNCT ejpam-6732 82 4 bmo bmo NOUN ejpam-6732 82 5 space space NOUN ejpam-6732 82 6 ) ) PUNCT ejpam-6732 82 7 . . PUNCT ejpam-6732 83 1 let let VERB ejpam-6732 83 2 h h NOUN ejpam-6732 83 3 is be AUX ejpam-6732 83 4 a a DET ejpam-6732 83 5 locally locally ADV ejpam-6732 83 6 integrable integrable ADJ ejpam-6732 83 7 function function NOUN ejpam-6732 83 8 then then ADV ejpam-6732 83 9 a a DET ejpam-6732 83 10 bmo bmo NOUN ejpam-6732 83 11 function function NOUN ejpam-6732 83 12 is be AUX ejpam-6732 83 13 consist consist VERB ejpam-6732 83 14 of of ADP ejpam-6732 83 15 those those DET ejpam-6732 83 16 functions function NOUN ejpam-6732 83 17 whose whose DET ejpam-6732 83 18 mean mean VERB ejpam-6732 83 19 oscillation oscillation NOUN ejpam-6732 83 20 given give VERB ejpam-6732 83 21 by by ADP ejpam-6732 83 22 1 1 NUM ejpam-6732 83 23 |b| |b| PROPN ejpam-6732 83 24 ∫ ∫ PROPN ejpam-6732 84 1 b b PROPN ejpam-6732 84 2 |h(i)−hb|di |h(i)−hb|di PROPN ejpam-6732 84 3 is be AUX ejpam-6732 84 4 bounded bound VERB ejpam-6732 84 5 . . PUNCT ejpam-6732 85 1 a a DET ejpam-6732 85 2 mathematically mathematically ADV ejpam-6732 85 3 , , PUNCT ejpam-6732 85 4 ∥h∥bmo ∥h∥bmo X ejpam-6732 85 5 = = SYM ejpam-6732 85 6 sup sup PROPN ejpam-6732 85 7 b b NOUN ejpam-6732 85 8 1 1 NUM ejpam-6732 85 9 |b| |b| PROPN ejpam-6732 85 10 ∫ ∫ PROPN ejpam-6732 85 11 b b PROPN ejpam-6732 85 12 |h(i)− |h(i)− PROPN ejpam-6732 85 13 hb|di hb|di VERB ejpam-6732 85 14 < < X ejpam-6732 85 15 ∞. ∞. PROPN ejpam-6732 85 16 b. b. PROPN ejpam-6732 85 17 sultan sultan PROPN ejpam-6732 85 18 et et PROPN ejpam-6732 85 19 al al PROPN ejpam-6732 85 20 . . PUNCT ejpam-6732 85 21 / / SYM ejpam-6732 85 22 eur eur PROPN ejpam-6732 85 23 . . PUNCT ejpam-6732 86 1 j. j. PROPN ejpam-6732 86 2 pure pure PROPN ejpam-6732 86 3 appl appl PROPN ejpam-6732 86 4 . . PROPN ejpam-6732 86 5 math math PROPN ejpam-6732 86 6 , , PUNCT ejpam-6732 86 7 18 18 NUM ejpam-6732 86 8 ( ( PUNCT ejpam-6732 86 9 4 4 NUM ejpam-6732 86 10 ) ) PUNCT ejpam-6732 86 11 ( ( PUNCT ejpam-6732 86 12 2025 2025 NUM ejpam-6732 86 13 ) ) PUNCT ejpam-6732 86 14 , , PUNCT ejpam-6732 86 15 6732 6732 NUM ejpam-6732 86 16 5 5 NUM ejpam-6732 86 17 of of ADP ejpam-6732 86 18 20 20 NUM ejpam-6732 86 19 lemma lemma PROPN ejpam-6732 86 20 6 6 NUM ejpam-6732 86 21 . . PUNCT ejpam-6732 87 1 [ [ X ejpam-6732 87 2 33 33 NUM ejpam-6732 87 3 ] ] PUNCT ejpam-6732 87 4 let let VERB ejpam-6732 87 5 j j PROPN ejpam-6732 87 6 , , PUNCT ejpam-6732 87 7 i i PROPN ejpam-6732 87 8 ∈ ∈ PROPN ejpam-6732 87 9 z z VERB ejpam-6732 87 10 for for ADP ejpam-6732 87 11 i i PRON ejpam-6732 87 12 < < X ejpam-6732 87 13 ℓ ℓ PROPN ejpam-6732 87 14 , , PUNCT ejpam-6732 87 15 and and CCONJ ejpam-6732 87 16 h h PROPN ejpam-6732 87 17 ∈ ∈ PROPN ejpam-6732 87 18 bmo(rn bmo(rn PROPN ejpam-6732 87 19 ) ) PUNCT ejpam-6732 87 20 , , PUNCT ejpam-6732 87 21 then then ADV ejpam-6732 87 22 1 1 NUM ejpam-6732 87 23 c c X ejpam-6732 87 24 ∥h∥nbmo ∥h∥nbmo X ejpam-6732 87 25 ≤ ≤ NUM ejpam-6732 87 26 sup sup PROPN ejpam-6732 87 27 b b NOUN ejpam-6732 87 28 : : PUNCT ejpam-6732 87 29 ball ball NOUN ejpam-6732 87 30 1 1 NUM ejpam-6732 87 31 ∥χb∥p ∥χb∥p PROPN ejpam-6732 87 32 ( ( PUNCT ejpam-6732 87 33 · · PUNCT ejpam-6732 87 34 ) ) PUNCT ejpam-6732 87 35 ∥(h− ∥(h− NOUN ejpam-6732 87 36 hb hb PROPN ejpam-6732 87 37 ) ) PUNCT ejpam-6732 87 38 nχb∥p nχb∥p PROPN ejpam-6732 87 39 ( ( PUNCT ejpam-6732 87 40 · · PUNCT ejpam-6732 87 41 ) ) PUNCT ejpam-6732 87 42 ( ( PUNCT ejpam-6732 87 43 1.8 1.8 NUM ejpam-6732 87 44 ) ) PUNCT ejpam-6732 87 45 ≤c∥h∥nbmo ≤c∥h∥nbmo PROPN ejpam-6732 87 46 , , PUNCT ejpam-6732 87 47 ( ( PUNCT ejpam-6732 87 48 1.9 1.9 NUM ejpam-6732 87 49 ) ) PUNCT ejpam-6732 87 50 ||(h− ||(h− PROPN ejpam-6732 87 51 hbi hbi PROPN ejpam-6732 87 52 ) ) PUNCT ejpam-6732 87 53 nχbk nχbk PROPN ejpam-6732 87 54 ||p ||p PROPN ejpam-6732 87 55 ( ( PUNCT ejpam-6732 87 56 · · PUNCT ejpam-6732 87 57 ) ) PUNCT ejpam-6732 87 58 ≤ ≤ NUM ejpam-6732 88 1 c(k c(k PROPN ejpam-6732 88 2 − − PROPN ejpam-6732 88 3 i)n||b||nbmo||χbk i)n||b||nbmo||χbk ADJ ejpam-6732 88 4 ||p ||p PROPN ejpam-6732 88 5 ( ( PUNCT ejpam-6732 88 6 · · PUNCT ejpam-6732 88 7 ) ) PUNCT ejpam-6732 88 8 . . PUNCT ejpam-6732 89 1 ( ( PUNCT ejpam-6732 89 2 1.10 1.10 NUM ejpam-6732 89 3 ) ) PUNCT ejpam-6732 89 4 lemma lemma PROPN ejpam-6732 89 5 7 7 NUM ejpam-6732 89 6 ( ( PUNCT ejpam-6732 89 7 [ [ X ejpam-6732 89 8 35 35 NUM ejpam-6732 89 9 ] ] PUNCT ejpam-6732 89 10 ) ) PUNCT ejpam-6732 89 11 . . PUNCT ejpam-6732 90 1 if if SCONJ ejpam-6732 90 2 a a DET ejpam-6732 90 3 > > X ejpam-6732 90 4 0 0 NUM ejpam-6732 90 5 , , PUNCT ejpam-6732 90 6 s s VERB ejpam-6732 90 7 ∈ ∈ PROPN ejpam-6732 91 1 [ [ X ejpam-6732 91 2 1,∞ 1,∞ NUM ejpam-6732 91 3 ] ] X ejpam-6732 91 4 , , PUNCT ejpam-6732 91 5 0 0 PUNCT ejpam-6732 91 6 < < X ejpam-6732 91 7 d d X ejpam-6732 91 8 ≤ ≤ PROPN ejpam-6732 91 9 s s X ejpam-6732 91 10 and and CCONJ ejpam-6732 91 11 −m+ −m+ NOUN ejpam-6732 91 12 ( ( PUNCT ejpam-6732 91 13 m− m− PROPN ejpam-6732 91 14 1)ds 1)ds NUM ejpam-6732 91 15 < < X ejpam-6732 91 16 u u X ejpam-6732 91 17 < < X ejpam-6732 91 18 ∞ ∞ PROPN ejpam-6732 91 19 , , PUNCT ejpam-6732 91 20 then then NUM ejpam-6732 91 21 ∫ ∫ PROPN ejpam-6732 91 22 |z2|≤a|z1| |z2|≤a|z1| PROPN ejpam-6732 91 23 |z2|u|φ(z1 |z2|u|φ(z1 NOUN ejpam-6732 91 24 − − PROPN ejpam-6732 92 1 z2)|ddz2 z2)|ddz2 PROPN ejpam-6732 92 2   PROPN ejpam-6732 92 3 1 1 NUM ejpam-6732 92 4 / / SYM ejpam-6732 92 5 d d NOUN ejpam-6732 92 6 ≤ ≤ NOUN ejpam-6732 92 7 |z1|(u+m)/d |z1|(u+m)/d PUNCT ejpam-6732 92 8 ∥φ∥ls(sm−1 ∥φ∥ls(sm−1 PROPN ejpam-6732 92 9 ) ) PUNCT ejpam-6732 92 10 . . PUNCT ejpam-6732 93 1 definition definition NOUN ejpam-6732 93 2 8 8 NUM ejpam-6732 93 3 . . PUNCT ejpam-6732 94 1 let let VERB ejpam-6732 94 2 0 0 PUNCT ejpam-6732 94 3 < < X ejpam-6732 94 4 p p X ejpam-6732 94 5 ≤ ≤ NUM ejpam-6732 94 6 ∞ ∞ PROPN ejpam-6732 94 7 , , PUNCT ejpam-6732 94 8 q q PROPN ejpam-6732 94 9 ∈ ∈ PROPN ejpam-6732 94 10 p(rn p(rn PROPN ejpam-6732 94 11 ) ) PUNCT ejpam-6732 94 12 , , PUNCT ejpam-6732 94 13 α α PROPN ejpam-6732 94 14 : : PUNCT ejpam-6732 94 15 rn rn PROPN ejpam-6732 94 16 → → SYM ejpam-6732 94 17 r r NOUN ejpam-6732 94 18 with with ADP ejpam-6732 94 19 α α PROPN ejpam-6732 94 20 ( ( PUNCT ejpam-6732 94 21 · · PUNCT ejpam-6732 94 22 ) ) PUNCT ejpam-6732 94 23 ∈ ∈ PROPN ejpam-6732 94 24 l∞(rn l∞(rn PROPN ejpam-6732 94 25 ) ) PUNCT ejpam-6732 94 26 . . PUNCT ejpam-6732 95 1 the the DET ejpam-6732 95 2 inhomogeneous inhomogeneous ADJ ejpam-6732 95 3 herz herz PROPN ejpam-6732 95 4 space space NOUN ejpam-6732 95 5 k k PROPN ejpam-6732 95 6 α α PROPN ejpam-6732 95 7 ( ( PUNCT ejpam-6732 95 8 · · PUNCT ejpam-6732 95 9 ) ) PUNCT ejpam-6732 95 10 p p NOUN ejpam-6732 95 11 , , PUNCT ejpam-6732 95 12 q(·)(r q(·)(r NOUN ejpam-6732 95 13 n n CCONJ ejpam-6732 95 14 ) ) PUNCT ejpam-6732 95 15 consists consist VERB ejpam-6732 95 16 of of ADP ejpam-6732 95 17 all all DET ejpam-6732 95 18 f f PROPN ejpam-6732 95 19 ∈ ∈ PROPN ejpam-6732 95 20 l l NOUN ejpam-6732 95 21 q q X ejpam-6732 95 22 ( ( PUNCT ejpam-6732 95 23 · · PUNCT ejpam-6732 95 24 ) ) PUNCT ejpam-6732 95 25 loc loc NOUN ejpam-6732 95 26 ( ( PUNCT ejpam-6732 95 27 r r NOUN ejpam-6732 95 28 n n CCONJ ejpam-6732 95 29 \ \ NOUN ejpam-6732 95 30 { { PUNCT ejpam-6732 95 31 0 0 NUM ejpam-6732 95 32 } } PUNCT ejpam-6732 95 33 ) ) PUNCT ejpam-6732 96 1 such such ADJ ejpam-6732 96 2 that that SCONJ ejpam-6732 96 3 ∥f∥ ∥f∥ PROPN ejpam-6732 96 4 k k PROPN ejpam-6732 96 5 α α PROPN ejpam-6732 96 6 ( ( PUNCT ejpam-6732 96 7 · · PUNCT ejpam-6732 96 8 ) ) PUNCT ejpam-6732 96 9 p p NOUN ejpam-6732 96 10 , , PUNCT ejpam-6732 96 11 q(·)(r q(·)(r NOUN ejpam-6732 96 12 n n CCONJ ejpam-6732 96 13 ) ) PUNCT ejpam-6732 96 14 : : PUNCT ejpam-6732 96 15 = = SYM ejpam-6732 96 16 ∥fχb0∥lq ∥fχb0∥lq PROPN ejpam-6732 96 17 ( ( PUNCT ejpam-6732 96 18 · · PUNCT ejpam-6732 96 19 ) ) PUNCT ejpam-6732 96 20 + + CCONJ ejpam-6732 96 21 ∑ ∑ NOUN ejpam-6732 96 22 k≥1 k≥1 NOUN ejpam-6732 96 23 ∥∥∥2α(·)fχk ∥∥∥2α(·)fχk X ejpam-6732 96 24 ∥∥∥p ∥∥∥p ADJ ejpam-6732 96 25 q q PROPN ejpam-6732 96 26 ( ( PUNCT ejpam-6732 96 27 · · PUNCT ejpam-6732 96 28 ) ) PUNCT ejpam-6732 97 1 1 1 PROPN ejpam-6732 97 2 / / SYM ejpam-6732 97 3 p p X ejpam-6732 97 4 < < X ejpam-6732 97 5 ∞. ∞. PROPN ejpam-6732 97 6 the the DET ejpam-6732 97 7 homogeneous homogeneous ADJ ejpam-6732 97 8 herz herz PROPN ejpam-6732 97 9 space space NOUN ejpam-6732 97 10 k̇ k̇ PROPN ejpam-6732 98 1 α α PROPN ejpam-6732 98 2 ( ( PUNCT ejpam-6732 98 3 · · PUNCT ejpam-6732 98 4 ) ) PUNCT ejpam-6732 99 1 p p NOUN ejpam-6732 99 2 , , PUNCT ejpam-6732 99 3 q(·)(r q(·)(r NOUN ejpam-6732 99 4 n n CCONJ ejpam-6732 99 5 ) ) PUNCT ejpam-6732 99 6 consists consist VERB ejpam-6732 99 7 of of ADP ejpam-6732 99 8 all all DET ejpam-6732 99 9 f f PROPN ejpam-6732 99 10 ∈ ∈ PROPN ejpam-6732 99 11 l l NOUN ejpam-6732 99 12 q q X ejpam-6732 99 13 ( ( PUNCT ejpam-6732 99 14 · · PUNCT ejpam-6732 99 15 ) ) PUNCT ejpam-6732 99 16 loc loc NOUN ejpam-6732 99 17 ( ( PUNCT ejpam-6732 99 18 r r NOUN ejpam-6732 99 19 n n CCONJ ejpam-6732 99 20 \ \ NOUN ejpam-6732 99 21 { { PUNCT ejpam-6732 99 22 0 0 NUM ejpam-6732 99 23 } } PUNCT ejpam-6732 99 24 ) ) PUNCT ejpam-6732 100 1 such such ADJ ejpam-6732 100 2 that that DET ejpam-6732 100 3 ∥f∥ ∥f∥ ADJ ejpam-6732 100 4 k̇ k̇ PROPN ejpam-6732 100 5 α α PROPN ejpam-6732 100 6 ( ( PUNCT ejpam-6732 100 7 · · PUNCT ejpam-6732 100 8 ) ) PUNCT ejpam-6732 100 9 p p NOUN ejpam-6732 100 10 , , PUNCT ejpam-6732 100 11 q(·)(r q(·)(r NOUN ejpam-6732 100 12 n n CCONJ ejpam-6732 100 13 ) ) PUNCT ejpam-6732 100 14 : : PUNCT ejpam-6732 100 15 = = SYM ejpam-6732 100 16 ( ( PUNCT ejpam-6732 100 17 ∑ ∑ ADV ejpam-6732 100 18 k∈z k∈z VERB ejpam-6732 100 19 ∥∥∥2α(·)fχk ∥∥∥2α(·)fχk NOUN ejpam-6732 100 20 ∥∥∥p ∥∥∥p ADJ ejpam-6732 100 21 q q PROPN ejpam-6732 100 22 ( ( PUNCT ejpam-6732 100 23 · · PUNCT ejpam-6732 100 24 ) ) PUNCT ejpam-6732 100 25 ) ) PUNCT ejpam-6732 100 26 1 1 X ejpam-6732 100 27 / / SYM ejpam-6732 100 28 p p X ejpam-6732 100 29 < < X ejpam-6732 100 30 ∞. ∞. PROPN ejpam-6732 100 31 next next ADV ejpam-6732 100 32 we we PRON ejpam-6732 100 33 give give VERB ejpam-6732 100 34 the the DET ejpam-6732 100 35 definition definition NOUN ejpam-6732 100 36 of of ADP ejpam-6732 100 37 variable variable ADJ ejpam-6732 100 38 herz herz ADJ ejpam-6732 100 39 - - PUNCT ejpam-6732 100 40 morrey morrey PROPN ejpam-6732 100 41 spaces space NOUN ejpam-6732 100 42 . . PUNCT ejpam-6732 101 1 definition definition NOUN ejpam-6732 101 2 9 9 NUM ejpam-6732 101 3 . . PUNCT ejpam-6732 102 1 let let VERB ejpam-6732 102 2 p p NOUN ejpam-6732 102 3 : : PUNCT ejpam-6732 102 4 rn rn PROPN ejpam-6732 102 5 → → PROPN ejpam-6732 102 6 [ [ X ejpam-6732 102 7 1,∞ 1,∞ NUM ejpam-6732 102 8 ) ) PUNCT ejpam-6732 102 9 , , PUNCT ejpam-6732 102 10 α α X ejpam-6732 102 11 ( ( PUNCT ejpam-6732 102 12 · · PUNCT ejpam-6732 102 13 ) ) PUNCT ejpam-6732 102 14 ∈ ∈ PROPN ejpam-6732 102 15 l∞(rn l∞(rn PROPN ejpam-6732 102 16 ) ) PUNCT ejpam-6732 102 17 , , PUNCT ejpam-6732 103 1 u u PROPN ejpam-6732 103 2 ∈ ∈ PROPN ejpam-6732 103 3 [ [ X ejpam-6732 103 4 1,∞ 1,∞ NUM ejpam-6732 103 5 ) ) PUNCT ejpam-6732 103 6 , , PUNCT ejpam-6732 103 7 and and CCONJ ejpam-6732 103 8 0 0 NUM ejpam-6732 103 9 ≤ ≤ NUM ejpam-6732 103 10 γ γ X ejpam-6732 103 11 < < X ejpam-6732 103 12 ∞. ∞. PROPN ejpam-6732 103 13 the the DET ejpam-6732 103 14 norm norm NOUN ejpam-6732 103 15 of of ADP ejpam-6732 103 16 variable variable ADJ ejpam-6732 103 17 herz herz ADJ ejpam-6732 103 18 - - PUNCT ejpam-6732 103 19 morrey morrey PROPN ejpam-6732 103 20 spaces space NOUN ejpam-6732 103 21 are be AUX ejpam-6732 103 22 defined define VERB ejpam-6732 103 23 as as ADP ejpam-6732 103 24 : : PUNCT ejpam-6732 103 25 mk̇ mk̇ NOUN ejpam-6732 104 1 α(·),u α(·),u NUM ejpam-6732 104 2 γ γ X ejpam-6732 104 3 , , PUNCT ejpam-6732 104 4 p p X ejpam-6732 104 5 ( ( PUNCT ejpam-6732 104 6 · · PUNCT ejpam-6732 104 7 ) ) PUNCT ejpam-6732 104 8 ( ( PUNCT ejpam-6732 104 9 r r NOUN ejpam-6732 104 10 n n CCONJ ejpam-6732 104 11 ) ) PUNCT ejpam-6732 104 12 = = PRON ejpam-6732 104 13 { { PUNCT ejpam-6732 104 14 g g PROPN ejpam-6732 104 15 ∈ ∈ PROPN ejpam-6732 104 16 l l NOUN ejpam-6732 104 17 p p X ejpam-6732 104 18 ( ( PUNCT ejpam-6732 104 19 · · PUNCT ejpam-6732 104 20 ) ) PUNCT ejpam-6732 104 21 loc loc NOUN ejpam-6732 104 22 ( ( PUNCT ejpam-6732 104 23 r r NOUN ejpam-6732 104 24 n n CCONJ ejpam-6732 104 25 \ \ NOUN ejpam-6732 104 26 { { PUNCT ejpam-6732 104 27 0 0 NUM ejpam-6732 104 28 } } PUNCT ejpam-6732 104 29 ) ) PUNCT ejpam-6732 104 30 : : PUNCT ejpam-6732 104 31 ∥g∥ ∥g∥ PROPN ejpam-6732 105 1 mk̇ mk̇ NOUN ejpam-6732 106 1 α(·),u α(·),u NUM ejpam-6732 106 2 γ γ X ejpam-6732 106 3 , , PUNCT ejpam-6732 106 4 p p X ejpam-6732 106 5 ( ( PUNCT ejpam-6732 106 6 · · PUNCT ejpam-6732 106 7 ) ) PUNCT ejpam-6732 106 8 ( ( PUNCT ejpam-6732 106 9 r r NOUN ejpam-6732 106 10 n n CCONJ ejpam-6732 106 11 ) ) PUNCT ejpam-6732 106 12 < < X ejpam-6732 106 13 ∞ ∞ PROPN ejpam-6732 106 14 } } PUNCT ejpam-6732 106 15 , , PUNCT ejpam-6732 106 16 where where SCONJ ejpam-6732 106 17 ∥g∥ ∥g∥ PROPN ejpam-6732 106 18 mk̇ mk̇ ADJ ejpam-6732 106 19 α(·),u α(·),u NUM ejpam-6732 106 20 γ γ X ejpam-6732 106 21 , , PUNCT ejpam-6732 106 22 p p X ejpam-6732 106 23 ( ( PUNCT ejpam-6732 106 24 · · PUNCT ejpam-6732 106 25 ) ) PUNCT ejpam-6732 106 26 ( ( PUNCT ejpam-6732 106 27 r r NOUN ejpam-6732 106 28 n n CCONJ ejpam-6732 106 29 ) ) PUNCT ejpam-6732 106 30 = = PUNCT ejpam-6732 107 1 sup sup NOUN ejpam-6732 107 2 m0∈z m0∈z PROPN ejpam-6732 108 1 2−m0γ 2−m0γ PROPN ejpam-6732 108 2 ( ( PUNCT ejpam-6732 108 3 m0∑ m0∑ PROPN ejpam-6732 108 4 k=−∞ k=−∞ PROPN ejpam-6732 109 1 ∥2kα(·)gχk∥up ∥2kα(·)gχk∥up PROPN ejpam-6732 109 2 ( ( PUNCT ejpam-6732 109 3 · · PUNCT ejpam-6732 109 4 ) ) PUNCT ejpam-6732 109 5 ) ) PUNCT ejpam-6732 109 6 1 1 NUM ejpam-6732 109 7 u u NOUN ejpam-6732 109 8 . . PUNCT ejpam-6732 110 1 for for ADP ejpam-6732 110 2 γ γ X ejpam-6732 110 3 = = SYM ejpam-6732 110 4 0 0 NUM ejpam-6732 110 5 , , PUNCT ejpam-6732 110 6 variable variable ADJ ejpam-6732 110 7 herz herz ADJ ejpam-6732 110 8 - - PUNCT ejpam-6732 110 9 morrey morrey PROPN ejpam-6732 110 10 spaces space NOUN ejpam-6732 110 11 becomes become VERB ejpam-6732 110 12 variable variable ADJ ejpam-6732 110 13 herz herz ADJ ejpam-6732 110 14 spaces space NOUN ejpam-6732 110 15 . . PUNCT ejpam-6732 111 1 the the DET ejpam-6732 111 2 next next ADJ ejpam-6732 111 3 proposition proposition NOUN ejpam-6732 111 4 is be AUX ejpam-6732 111 5 the the DET ejpam-6732 111 6 generalization generalization NOUN ejpam-6732 111 7 of of ADP ejpam-6732 111 8 variable variable ADJ ejpam-6732 111 9 exponents exponent NOUN ejpam-6732 111 10 herz herz PROPN ejpam-6732 111 11 spaces space VERB ejpam-6732 111 12 in in ADP ejpam-6732 111 13 [ [ X ejpam-6732 111 14 2 2 NUM ejpam-6732 111 15 ] ] PUNCT ejpam-6732 111 16 . . PUNCT ejpam-6732 112 1 proposition proposition NOUN ejpam-6732 112 2 10 10 NUM ejpam-6732 112 3 . . PUNCT ejpam-6732 113 1 let let VERB ejpam-6732 113 2 α α PRON ejpam-6732 113 3 , , PUNCT ejpam-6732 113 4 u u NOUN ejpam-6732 113 5 , , PUNCT ejpam-6732 113 6 p p NOUN ejpam-6732 113 7 are be AUX ejpam-6732 113 8 as as ADV ejpam-6732 113 9 defined define VERB ejpam-6732 113 10 in in ADP ejpam-6732 113 11 definition definition NOUN ejpam-6732 113 12 9 9 NUM ejpam-6732 113 13 , , PUNCT ejpam-6732 113 14 then then ADV ejpam-6732 113 15 ∥f∥ ∥f∥ PROPN ejpam-6732 114 1 mk̇ mk̇ PROPN ejpam-6732 114 2 α(·),u α(·),u NUM ejpam-6732 114 3 γ γ PROPN ejpam-6732 114 4 , , PUNCT ejpam-6732 114 5 p p X ejpam-6732 114 6 ( ( PUNCT ejpam-6732 114 7 · · PUNCT ejpam-6732 114 8 ) ) PUNCT ejpam-6732 114 9 ( ( PUNCT ejpam-6732 114 10 r r NOUN ejpam-6732 114 11 n n CCONJ ejpam-6732 114 12 ) ) PUNCT ejpam-6732 114 13 = = PUNCT ejpam-6732 115 1 sup sup NOUN ejpam-6732 115 2 m0∈z m0∈z PROPN ejpam-6732 116 1 2−m0γ 2−m0γ PROPN ejpam-6732 116 2 ( ( PUNCT ejpam-6732 116 3 m0∑ m0∑ PROPN ejpam-6732 116 4 k=−∞ k=−∞ PROPN ejpam-6732 116 5 ∥2kα(·)fχk∥up ∥2kα(·)fχk∥up PROPN ejpam-6732 116 6 ( ( PUNCT ejpam-6732 116 7 · · PUNCT ejpam-6732 116 8 ) ) PUNCT ejpam-6732 116 9 ) ) PUNCT ejpam-6732 116 10 1 1 NUM ejpam-6732 116 11 u u PROPN ejpam-6732 116 12 b. b. PROPN ejpam-6732 116 13 sultan sultan PROPN ejpam-6732 116 14 et et PROPN ejpam-6732 116 15 al al PROPN ejpam-6732 116 16 . . PUNCT ejpam-6732 116 17 / / SYM ejpam-6732 116 18 eur eur PROPN ejpam-6732 116 19 . . PUNCT ejpam-6732 117 1 j. j. PROPN ejpam-6732 117 2 pure pure PROPN ejpam-6732 117 3 appl appl PROPN ejpam-6732 117 4 . . PROPN ejpam-6732 117 5 math math PROPN ejpam-6732 117 6 , , PUNCT ejpam-6732 117 7 18 18 NUM ejpam-6732 117 8 ( ( PUNCT ejpam-6732 117 9 4 4 NUM ejpam-6732 117 10 ) ) PUNCT ejpam-6732 117 11 ( ( PUNCT ejpam-6732 117 12 2025 2025 NUM ejpam-6732 117 13 ) ) PUNCT ejpam-6732 117 14 , , PUNCT ejpam-6732 117 15 6732 6732 NUM ejpam-6732 117 16 6 6 NUM ejpam-6732 117 17 of of ADP ejpam-6732 117 18 20 20 NUM ejpam-6732 117 19 ≈max ≈max NUM ejpam-6732 117 20   PUNCT ejpam-6732 117 21 sup sup NOUN ejpam-6732 117 22 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 117 23 2−m0γ 2−m0γ NUM ejpam-6732 118 1 ( ( PUNCT ejpam-6732 118 2 −1∑ −1∑ PROPN ejpam-6732 118 3 k=−∞ k=−∞ PROPN ejpam-6732 118 4 2kα(0)u∥fχk∥up 2kα(0)u∥fχk∥up PROPN ejpam-6732 118 5 ( ( PUNCT ejpam-6732 118 6 · · PUNCT ejpam-6732 118 7 ) ) PUNCT ejpam-6732 118 8 ) ) PUNCT ejpam-6732 118 9 1 1 NUM ejpam-6732 118 10 u u NOUN ejpam-6732 118 11 , , PUNCT ejpam-6732 118 12 sup sup PROPN ejpam-6732 118 13 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 118 14 2−m0γ 2−m0γ PROPN ejpam-6732 118 15 ( ( PUNCT ejpam-6732 118 16 −1∑ −1∑ PROPN ejpam-6732 118 17 k=−∞ k=−∞ PROPN ejpam-6732 118 18 2kα(0)u∥fχk∥up 2kα(0)u∥fχk∥up PROPN ejpam-6732 118 19 ( ( PUNCT ejpam-6732 118 20 · · PUNCT ejpam-6732 118 21 ) ) PUNCT ejpam-6732 118 22 ) ) PUNCT ejpam-6732 118 23 1 1 NUM ejpam-6732 118 24 u u NOUN ejpam-6732 118 25 + + NOUN ejpam-6732 118 26 sup sup PROPN ejpam-6732 118 27 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 118 28 2−m0γ 2−m0γ PROPN ejpam-6732 118 29 ( ( PUNCT ejpam-6732 118 30 m0∑ m0∑ PROPN ejpam-6732 118 31 k=0 k=0 PROPN ejpam-6732 118 32 2kα∞u∥fχk∥up 2kα∞u∥fχk∥up NUM ejpam-6732 118 33 ( ( PUNCT ejpam-6732 118 34 · · PUNCT ejpam-6732 118 35 ) ) PUNCT ejpam-6732 118 36 ) ) PUNCT ejpam-6732 118 37 1 1 NUM ejpam-6732 118 38 u u NOUN ejpam-6732 118 39   PROPN ejpam-6732 118 40 2 2 NUM ejpam-6732 118 41 . . PUNCT ejpam-6732 119 1 the the DET ejpam-6732 119 2 atomic atomic ADJ ejpam-6732 119 3 characterization characterization NOUN ejpam-6732 119 4 let let VERB ejpam-6732 119 5 s s PROPN ejpam-6732 119 6 ( ( PUNCT ejpam-6732 119 7 rn rn NOUN ejpam-6732 119 8 ) ) PUNCT ejpam-6732 119 9 denotes denote VERB ejpam-6732 119 10 the the DET ejpam-6732 119 11 schwartz schwartz PROPN ejpam-6732 119 12 space space NOUN ejpam-6732 119 13 of of ADP ejpam-6732 119 14 all all PRON ejpam-6732 119 15 rapidly rapidly ADV ejpam-6732 119 16 decreasing decrease VERB ejpam-6732 119 17 infinitely infinitely ADV ejpam-6732 119 18 differentiable differentiable ADJ ejpam-6732 119 19 functions function NOUN ejpam-6732 119 20 on on ADP ejpam-6732 119 21 rn rn PROPN ejpam-6732 119 22 , , PUNCT ejpam-6732 119 23 and and CCONJ ejpam-6732 119 24 s s VERB ejpam-6732 119 25 ′ ′ NUM ejpam-6732 119 26 ( ( PUNCT ejpam-6732 119 27 rn rn NOUN ejpam-6732 119 28 ) ) PUNCT ejpam-6732 119 29 denotes denote VERB ejpam-6732 119 30 the the DET ejpam-6732 119 31 dual dual ADJ ejpam-6732 119 32 space space NOUN ejpam-6732 119 33 of of ADP ejpam-6732 119 34 s s PROPN ejpam-6732 119 35 ( ( PUNCT ejpam-6732 119 36 rn rn NOUN ejpam-6732 119 37 ) ) PUNCT ejpam-6732 119 38 . . PUNCT ejpam-6732 120 1 let let VERB ejpam-6732 120 2 gng gng PROPN ejpam-6732 120 3 be be AUX ejpam-6732 120 4 the the DET ejpam-6732 120 5 grand grand ADJ ejpam-6732 120 6 maximal maximal ADJ ejpam-6732 120 7 function function NOUN ejpam-6732 120 8 of of ADP ejpam-6732 120 9 g g NOUN ejpam-6732 120 10 defined define VERB ejpam-6732 120 11 by by ADP ejpam-6732 120 12 gng(x gng(x NOUN ejpam-6732 120 13 ) ) PUNCT ejpam-6732 120 14 : : PUNCT ejpam-6732 121 1 = = NUM ejpam-6732 121 2 sup sup NOUN ejpam-6732 121 3 ϕ∈an ϕ∈an ADJ ejpam-6732 121 4 |ϕ∗ |ϕ∗ PROPN ejpam-6732 121 5 ∇(g)(x)| ∇(g)(x)| NOUN ejpam-6732 121 6 , , PUNCT ejpam-6732 121 7 x x PUNCT ejpam-6732 121 8 ∈ ∈ PROPN ejpam-6732 121 9 rn rn NOUN ejpam-6732 121 10 where where SCONJ ejpam-6732 121 11 an an DET ejpam-6732 121 12 : : PUNCT ejpam-6732 121 13 = = X ejpam-6732 121 14 { { PUNCT ejpam-6732 121 15 ϕ ϕ PROPN ejpam-6732 121 16 ∈ ∈ PROPN ejpam-6732 121 17 s s X ejpam-6732 121 18 ( ( PUNCT ejpam-6732 121 19 rn rn NOUN ejpam-6732 121 20 ) ) PUNCT ejpam-6732 121 21 : : PUNCT ejpam-6732 121 22 sup sup NOUN ejpam-6732 121 23 |α|,|β|≤n,∀x∈rn |α|,|β|≤n,∀x∈rn X ejpam-6732 121 24 ∣∣xαdβϕ(x ∣∣xαdβϕ(x PUNCT ejpam-6732 121 25 ) ) PUNCT ejpam-6732 121 26 ∣∣ ∣∣ NUM ejpam-6732 121 27 ≤ ≤ NUM ejpam-6732 121 28 1 1 NUM ejpam-6732 121 29 } } PUNCT ejpam-6732 121 30 and and CCONJ ejpam-6732 121 31 n n CCONJ ejpam-6732 121 32 > > SYM ejpam-6732 121 33 n+1 n+1 PROPN ejpam-6732 121 34 and and CCONJ ejpam-6732 121 35 ϕ∗ ϕ∗ PROPN ejpam-6732 121 36 ∇ ∇ X ejpam-6732 121 37 is be AUX ejpam-6732 121 38 the the DET ejpam-6732 121 39 nontangential nontangential ADJ ejpam-6732 121 40 maximal maximal ADJ ejpam-6732 121 41 operator operator NOUN ejpam-6732 121 42 defined define VERB ejpam-6732 121 43 by by ADP ejpam-6732 121 44 ϕ∗ ϕ∗ ADJ ejpam-6732 121 45 ∇(g)(x ∇(g)(x PROPN ejpam-6732 121 46 ) ) PUNCT ejpam-6732 122 1 : : PUNCT ejpam-6732 122 2 = = PUNCT ejpam-6732 122 3 sup sup NOUN ejpam-6732 122 4 |y−x| > X ejpam-6732 127 14 n+1 n+1 PROPN ejpam-6732 127 15 . . PUNCT ejpam-6732 128 1 the the DET ejpam-6732 128 2 herz herz PROPN ejpam-6732 128 3 - - PUNCT ejpam-6732 128 4 morrey morrey NOUN ejpam-6732 128 5 - - PUNCT ejpam-6732 128 6 hardy hardy ADJ ejpam-6732 128 7 space space NOUN ejpam-6732 128 8 with with ADP ejpam-6732 128 9 variable variable ADJ ejpam-6732 128 10 exponents exponent NOUN ejpam-6732 128 11 hmk̇ hmk̇ PROPN ejpam-6732 128 12 α(·),u α(·),u PROPN ejpam-6732 128 13 γ γ PROPN ejpam-6732 128 14 , , PUNCT ejpam-6732 128 15 p p X ejpam-6732 128 16 ( ( PUNCT ejpam-6732 128 17 · · PUNCT ejpam-6732 128 18 ) ) PUNCT ejpam-6732 128 19 ( ( PUNCT ejpam-6732 128 20 r r NOUN ejpam-6732 128 21 n n CCONJ ejpam-6732 128 22 ) ) PUNCT ejpam-6732 128 23 is be AUX ejpam-6732 128 24 defined define VERB ejpam-6732 128 25 by by ADP ejpam-6732 128 26 hmk̇ hmk̇ PROPN ejpam-6732 128 27 α(·),u α(·),u PROPN ejpam-6732 128 28 γ γ PROPN ejpam-6732 128 29 , , PUNCT ejpam-6732 128 30 p p X ejpam-6732 128 31 ( ( PUNCT ejpam-6732 128 32 · · PUNCT ejpam-6732 128 33 ) ) PUNCT ejpam-6732 128 34 ( ( PUNCT ejpam-6732 128 35 r r NOUN ejpam-6732 128 36 n n CCONJ ejpam-6732 128 37 ) ) PUNCT ejpam-6732 128 38 : : PUNCT ejpam-6732 129 1 = = X ejpam-6732 129 2 { { PUNCT ejpam-6732 129 3 g g PROPN ejpam-6732 129 4 ∈ ∈ PROPN ejpam-6732 129 5 s s PART ejpam-6732 129 6 ′ ′ NUM ejpam-6732 129 7 ( ( PUNCT ejpam-6732 129 8 rn rn NOUN ejpam-6732 129 9 ) ) PUNCT ejpam-6732 129 10 : : PUNCT ejpam-6732 129 11 ∥g∥ ∥g∥ PROPN ejpam-6732 130 1 mk̇ mk̇ NOUN ejpam-6732 131 1 α(·),u α(·),u NUM ejpam-6732 131 2 γ γ X ejpam-6732 131 3 , , PUNCT ejpam-6732 131 4 p p X ejpam-6732 131 5 ( ( PUNCT ejpam-6732 131 6 · · PUNCT ejpam-6732 131 7 ) ) PUNCT ejpam-6732 131 8 ( ( PUNCT ejpam-6732 131 9 r r NOUN ejpam-6732 131 10 n n CCONJ ejpam-6732 131 11 ) ) PUNCT ejpam-6732 131 12 : : PUNCT ejpam-6732 131 13 = = SYM ejpam-6732 131 14 ∥gng∥ ∥gng∥ X ejpam-6732 132 1 mk̇ mk̇ NOUN ejpam-6732 132 2 α(·),u α(·),u NUM ejpam-6732 132 3 γ γ X ejpam-6732 132 4 , , PUNCT ejpam-6732 132 5 p p X ejpam-6732 132 6 ( ( PUNCT ejpam-6732 132 7 · · PUNCT ejpam-6732 132 8 ) ) PUNCT ejpam-6732 132 9 ( ( PUNCT ejpam-6732 132 10 r r NOUN ejpam-6732 132 11 n n CCONJ ejpam-6732 132 12 ) ) PUNCT ejpam-6732 132 13 < < X ejpam-6732 132 14 ∞ ∞ NUM ejpam-6732 132 15 } } PUNCT ejpam-6732 132 16 . . PUNCT ejpam-6732 133 1 definition definition NOUN ejpam-6732 133 2 12 12 NUM ejpam-6732 133 3 . . PUNCT ejpam-6732 134 1 let let VERB ejpam-6732 135 1 p p PRON ejpam-6732 135 2 ( ( PUNCT ejpam-6732 135 3 · · PUNCT ejpam-6732 135 4 ) ) PUNCT ejpam-6732 135 5 ∈ ∈ PROPN ejpam-6732 135 6 p p X ejpam-6732 135 7 ( ( PUNCT ejpam-6732 135 8 rn rn NOUN ejpam-6732 135 9 ) ) PUNCT ejpam-6732 135 10 and and CCONJ ejpam-6732 135 11 α α PRON ejpam-6732 135 12 ( ( PUNCT ejpam-6732 135 13 · · PUNCT ejpam-6732 135 14 ) ) PUNCT ejpam-6732 135 15 ∈ ∈ PROPN ejpam-6732 135 16 l∞ l∞ NOUN ejpam-6732 135 17 ( ( PUNCT ejpam-6732 135 18 rn rn NOUN ejpam-6732 135 19 ) ) PUNCT ejpam-6732 135 20 be be AUX ejpam-6732 135 21 log log NOUN ejpam-6732 135 22 - - PUNCT ejpam-6732 135 23 hölder hölder NOUN ejpam-6732 135 24 continuous continuous ADJ ejpam-6732 135 25 both both CCONJ ejpam-6732 135 26 at at ADP ejpam-6732 135 27 the the DET ejpam-6732 135 28 origin origin NOUN ejpam-6732 135 29 and and CCONJ ejpam-6732 135 30 infinity infinity NOUN ejpam-6732 135 31 , , PUNCT ejpam-6732 135 32 and and CCONJ ejpam-6732 135 33 nonnegative nonnegative ADJ ejpam-6732 135 34 integer integer NOUN ejpam-6732 135 35 s s PART ejpam-6732 135 36 ⩾ ⩾ NOUN ejpam-6732 136 1 [ [ X ejpam-6732 136 2 αr αr INTJ ejpam-6732 136 3 − − PROPN ejpam-6732 136 4 nδ2 nδ2 PROPN ejpam-6732 136 5 ] ] X ejpam-6732 136 6 ; ; PUNCT ejpam-6732 136 7 here here ADV ejpam-6732 136 8 αr αr PROPN ejpam-6732 136 9 = = SYM ejpam-6732 136 10 α(0 α(0 PROPN ejpam-6732 136 11 ) ) PUNCT ejpam-6732 136 12 , , PUNCT ejpam-6732 136 13 if if SCONJ ejpam-6732 136 14 r r NOUN ejpam-6732 136 15 < < X ejpam-6732 136 16 1 1 NUM ejpam-6732 136 17 , , PUNCT ejpam-6732 136 18 and and CCONJ ejpam-6732 136 19 αr αr NUM ejpam-6732 136 20 = = SYM ejpam-6732 136 21 α∞ α∞ NOUN ejpam-6732 136 22 , , PUNCT ejpam-6732 136 23 if if SCONJ ejpam-6732 136 24 r r NOUN ejpam-6732 136 25 ⩾ ⩾ NOUN ejpam-6732 136 26 1 1 NUM ejpam-6732 136 27 , , PUNCT ejpam-6732 136 28 nδ2 nδ2 PROPN ejpam-6732 136 29 ≤ ≤ NUM ejpam-6732 136 30 αr αr ADP ejpam-6732 136 31 < < X ejpam-6732 136 32 ∞ ∞ PROPN ejpam-6732 136 33 and and CCONJ ejpam-6732 136 34 δ2 δ2 VERB ejpam-6732 136 35 as as ADP ejpam-6732 136 36 in in ADP ejpam-6732 136 37 lemma lemma PROPN ejpam-6732 136 38 3 3 NUM ejpam-6732 136 39 . . PUNCT ejpam-6732 137 1 ( ( PUNCT ejpam-6732 137 2 i i NOUN ejpam-6732 137 3 ) ) PUNCT ejpam-6732 137 4 a a DET ejpam-6732 137 5 function function NOUN ejpam-6732 137 6 a a PRON ejpam-6732 137 7 on on ADP ejpam-6732 137 8 rn rn PROPN ejpam-6732 137 9 is be AUX ejpam-6732 137 10 called call VERB ejpam-6732 137 11 a a DET ejpam-6732 137 12 central central ADJ ejpam-6732 137 13 ( ( PUNCT ejpam-6732 137 14 α α X ejpam-6732 137 15 ( ( PUNCT ejpam-6732 137 16 · · PUNCT ejpam-6732 137 17 ) ) PUNCT ejpam-6732 137 18 , , PUNCT ejpam-6732 137 19 p p X ejpam-6732 137 20 ( ( PUNCT ejpam-6732 137 21 · · PUNCT ejpam-6732 137 22 ) ) PUNCT ejpam-6732 137 23 ) ) PUNCT ejpam-6732 137 24 atom atom NOUN ejpam-6732 137 25 , , PUNCT ejpam-6732 137 26 if if SCONJ ejpam-6732 137 27 it it PRON ejpam-6732 137 28 satisfies satisfy VERB ejpam-6732 137 29 ( ( PUNCT ejpam-6732 137 30 1 1 X ejpam-6732 137 31 ) ) PUNCT ejpam-6732 137 32 supp supp NOUN ejpam-6732 137 33 a a DET ejpam-6732 137 34 ⊂ ⊂ PROPN ejpam-6732 137 35 b(0 b(0 PROPN ejpam-6732 137 36 , , PUNCT ejpam-6732 137 37 r r NOUN ejpam-6732 137 38 ) ) PUNCT ejpam-6732 137 39 , , PUNCT ejpam-6732 137 40 ( ( PUNCT ejpam-6732 137 41 2 2 X ejpam-6732 137 42 ) ) PUNCT ejpam-6732 137 43 ∥a∥p ∥a∥p PROPN ejpam-6732 137 44 ( ( PUNCT ejpam-6732 137 45 · · PUNCT ejpam-6732 137 46 ) ) PUNCT ejpam-6732 137 47 ≤ ≤ ADV ejpam-6732 137 48 |b(0 |b(0 ADJ ejpam-6732 137 49 , , PUNCT ejpam-6732 137 50 r)|−αr r)|−αr NOUN ejpam-6732 137 51 / / SYM ejpam-6732 137 52 n n CCONJ ejpam-6732 137 53 , , PUNCT ejpam-6732 137 54 ( ( PUNCT ejpam-6732 137 55 3 3 X ejpam-6732 137 56 ) ) PUNCT ejpam-6732 137 57 ∫ ∫ PROPN ejpam-6732 137 58 rn rn PROPN ejpam-6732 138 1 a(x)x a(x)x PROPN ejpam-6732 138 2 βdx βdx PROPN ejpam-6732 138 3 = = SYM ejpam-6732 138 4 0 0 NUM ejpam-6732 138 5 , , PUNCT ejpam-6732 138 6 |β| |β| NOUN ejpam-6732 138 7 ≤ ≤ PROPN ejpam-6732 138 8 s. s. PROPN ejpam-6732 138 9 b. b. PROPN ejpam-6732 138 10 sultan sultan PROPN ejpam-6732 138 11 et et PROPN ejpam-6732 139 1 al al PROPN ejpam-6732 139 2 . . PUNCT ejpam-6732 139 3 / / SYM ejpam-6732 139 4 eur eur PROPN ejpam-6732 139 5 . . PUNCT ejpam-6732 140 1 j. j. PROPN ejpam-6732 140 2 pure pure PROPN ejpam-6732 140 3 appl appl PROPN ejpam-6732 140 4 . . PROPN ejpam-6732 140 5 math math PROPN ejpam-6732 140 6 , , PUNCT ejpam-6732 140 7 18 18 NUM ejpam-6732 140 8 ( ( PUNCT ejpam-6732 140 9 4 4 NUM ejpam-6732 140 10 ) ) PUNCT ejpam-6732 140 11 ( ( PUNCT ejpam-6732 140 12 2025 2025 NUM ejpam-6732 140 13 ) ) PUNCT ejpam-6732 140 14 , , PUNCT ejpam-6732 140 15 6732 6732 NUM ejpam-6732 140 16 7 7 NUM ejpam-6732 140 17 of of ADP ejpam-6732 140 18 20 20 NUM ejpam-6732 140 19 ( ( PUNCT ejpam-6732 140 20 ii ii NOUN ejpam-6732 140 21 ) ) PUNCT ejpam-6732 140 22 a a DET ejpam-6732 140 23 function function NOUN ejpam-6732 140 24 a a PRON ejpam-6732 140 25 on on ADP ejpam-6732 140 26 rn rn PROPN ejpam-6732 140 27 is be AUX ejpam-6732 140 28 called call VERB ejpam-6732 140 29 a a DET ejpam-6732 140 30 central central ADJ ejpam-6732 140 31 ( ( PUNCT ejpam-6732 140 32 α α X ejpam-6732 140 33 ( ( PUNCT ejpam-6732 140 34 · · PUNCT ejpam-6732 140 35 ) ) PUNCT ejpam-6732 140 36 , , PUNCT ejpam-6732 140 37 p(·))-atom p(·))-atom NOUN ejpam-6732 140 38 of of ADP ejpam-6732 140 39 restricted restricted ADJ ejpam-6732 140 40 type type NOUN ejpam-6732 140 41 , , PUNCT ejpam-6732 140 42 if if SCONJ ejpam-6732 140 43 it it PRON ejpam-6732 140 44 satisfies satisfy VERB ejpam-6732 140 45 2 2 NUM ejpam-6732 140 46 , , PUNCT ejpam-6732 140 47 3 3 NUM ejpam-6732 140 48 and and CCONJ ejpam-6732 140 49 condition condition NOUN ejpam-6732 140 50 given give VERB ejpam-6732 140 51 below below ADP ejpam-6732 140 52 ( ( PUNCT ejpam-6732 140 53 a a PRON ejpam-6732 140 54 ) ) PUNCT ejpam-6732 140 55 supp supp PROPN ejpam-6732 140 56 α α PROPN ejpam-6732 140 57 ⊂ ⊂ PROPN ejpam-6732 140 58 b(0 b(0 PROPN ejpam-6732 140 59 , , PUNCT ejpam-6732 140 60 r r NOUN ejpam-6732 140 61 ) ) PUNCT ejpam-6732 140 62 , , PUNCT ejpam-6732 141 1 r r NOUN ejpam-6732 141 2 ⩾ ⩾ NOUN ejpam-6732 141 3 1 1 NUM ejpam-6732 141 4 . . X ejpam-6732 141 5 theorem theorem VERB ejpam-6732 141 6 13 13 NUM ejpam-6732 141 7 . . PUNCT ejpam-6732 142 1 [ [ X ejpam-6732 142 2 28 28 NUM ejpam-6732 142 3 ] ] X ejpam-6732 142 4 let let VERB ejpam-6732 142 5 0 0 NUM ejpam-6732 142 6 < < X ejpam-6732 142 7 u u X ejpam-6732 142 8 < < X ejpam-6732 142 9 ∞ ∞ PROPN ejpam-6732 142 10 , , PUNCT ejpam-6732 142 11 p p X ejpam-6732 142 12 ( ( PUNCT ejpam-6732 142 13 · · PUNCT ejpam-6732 142 14 ) ) PUNCT ejpam-6732 142 15 ∈ ∈ PROPN ejpam-6732 142 16 b b PROPN ejpam-6732 142 17 ( ( PUNCT ejpam-6732 142 18 rn rn NOUN ejpam-6732 142 19 ) ) PUNCT ejpam-6732 142 20 , , PUNCT ejpam-6732 142 21 0 0 NUM ejpam-6732 142 22 ≤ ≤ NUM ejpam-6732 142 23 γ γ X ejpam-6732 142 24 < < X ejpam-6732 142 25 ∞ ∞ PROPN ejpam-6732 142 26 , , PUNCT ejpam-6732 142 27 and and CCONJ ejpam-6732 142 28 α α PRON ejpam-6732 142 29 ( ( PUNCT ejpam-6732 142 30 · · PUNCT ejpam-6732 142 31 ) ) PUNCT ejpam-6732 142 32 ∈ ∈ PROPN ejpam-6732 142 33 l∞ l∞ NOUN ejpam-6732 142 34 ( ( PUNCT ejpam-6732 142 35 rn rn NOUN ejpam-6732 142 36 ) ) PUNCT ejpam-6732 142 37 be be AUX ejpam-6732 142 38 log log NOUN ejpam-6732 142 39 - - PUNCT ejpam-6732 142 40 hölder hölder NOUN ejpam-6732 142 41 continuous continuous ADJ ejpam-6732 142 42 both both CCONJ ejpam-6732 142 43 at at ADP ejpam-6732 142 44 the the DET ejpam-6732 142 45 origin origin NOUN ejpam-6732 142 46 and and CCONJ ejpam-6732 142 47 infinity infinity NOUN ejpam-6732 142 48 , , PUNCT ejpam-6732 142 49 2λ 2λ NUM ejpam-6732 142 50 ≤ ≤ ADV ejpam-6732 142 51 α α PROPN ejpam-6732 142 52 ( ( PUNCT ejpam-6732 142 53 · · PUNCT ejpam-6732 142 54 ) ) PUNCT ejpam-6732 142 55 , , PUNCT ejpam-6732 142 56 nδ2 nδ2 PROPN ejpam-6732 142 57 ≤ ≤ VERB ejpam-6732 142 58 α(0 α(0 PROPN ejpam-6732 142 59 ) ) PUNCT ejpam-6732 142 60 , , PUNCT ejpam-6732 142 61 α∞ α∞ VERB ejpam-6732 142 62 < < X ejpam-6732 142 63 ∞ ∞ PROPN ejpam-6732 142 64 , , PUNCT ejpam-6732 142 65 and and CCONJ ejpam-6732 142 66 δ2 δ2 VERB ejpam-6732 142 67 as as ADP ejpam-6732 142 68 in in ADP ejpam-6732 142 69 lemma lemma PROPN ejpam-6732 142 70 3 3 NUM ejpam-6732 142 71 . . PUNCT ejpam-6732 143 1 then then ADV ejpam-6732 143 2 f f PROPN ejpam-6732 143 3 ∈ ∈ PROPN ejpam-6732 143 4 hmk̇ hmk̇ PROPN ejpam-6732 143 5 α(·),u α(·),u PROPN ejpam-6732 143 6 γ γ X ejpam-6732 143 7 , , PUNCT ejpam-6732 143 8 p p X ejpam-6732 143 9 ( ( PUNCT ejpam-6732 143 10 · · PUNCT ejpam-6732 143 11 ) ) PUNCT ejpam-6732 143 12 ( ( PUNCT ejpam-6732 143 13 r r NOUN ejpam-6732 143 14 n n CCONJ ejpam-6732 143 15 ) ) PUNCT ejpam-6732 143 16 iff iff PROPN ejpam-6732 143 17 f f PROPN ejpam-6732 143 18 = = SYM ejpam-6732 143 19 ∑∞ ∑∞ NOUN ejpam-6732 143 20 k=−∞ k=−∞ X ejpam-6732 144 1 λkak λkak VERB ejpam-6732 144 2 in in ADP ejpam-6732 144 3 the the DET ejpam-6732 144 4 sense sense NOUN ejpam-6732 144 5 of of ADP ejpam-6732 144 6 s s PRON ejpam-6732 144 7 ′ ′ NUM ejpam-6732 144 8 ( ( PUNCT ejpam-6732 144 9 rn rn NOUN ejpam-6732 144 10 ) ) PUNCT ejpam-6732 144 11 , , PUNCT ejpam-6732 144 12 where where SCONJ ejpam-6732 144 13 each each DET ejpam-6732 144 14 ak ak PROPN ejpam-6732 144 15 is be AUX ejpam-6732 144 16 a a DET ejpam-6732 144 17 central central ADJ ejpam-6732 144 18 ( ( PUNCT ejpam-6732 144 19 α α X ejpam-6732 144 20 ( ( PUNCT ejpam-6732 144 21 · · PUNCT ejpam-6732 144 22 ) ) PUNCT ejpam-6732 144 23 , , PUNCT ejpam-6732 144 24 p(·))-atom p(·))-atom NOUN ejpam-6732 144 25 with with ADP ejpam-6732 144 26 support support NOUN ejpam-6732 144 27 contained contain VERB ejpam-6732 144 28 in in ADP ejpam-6732 144 29 bk bk NOUN ejpam-6732 144 30 and and CCONJ ejpam-6732 144 31 sup sup NOUN ejpam-6732 144 32 ϑ>0 ϑ>0 PROPN ejpam-6732 144 33 sup sup NOUN ejpam-6732 144 34 m0∈z m0∈z PROPN ejpam-6732 145 1 2−m0γ 2−m0γ NUM ejpam-6732 146 1 ∑m0 ∑m0 NUM ejpam-6732 146 2 k=−∞ k=−∞ PROPN ejpam-6732 146 3 |λk|u |λk|u X ejpam-6732 146 4 < < X ejpam-6732 146 5 ∞. ∞. PROPN ejpam-6732 146 6 moreover moreover ADV ejpam-6732 146 7 , , PUNCT ejpam-6732 146 8 ∥f∥ ∥f∥ ADJ ejpam-6732 146 9 hmk̇ hmk̇ PROPN ejpam-6732 146 10 α(·),u α(·),u PROPN ejpam-6732 146 11 γ γ PROPN ejpam-6732 146 12 , , PUNCT ejpam-6732 146 13 p p X ejpam-6732 146 14 ( ( PUNCT ejpam-6732 146 15 · · PUNCT ejpam-6732 146 16 ) ) PUNCT ejpam-6732 146 17 ( ( PUNCT ejpam-6732 146 18 r r NOUN ejpam-6732 146 19 n n CCONJ ejpam-6732 146 20 ) ) PUNCT ejpam-6732 147 1 ≈ ≈ PROPN ejpam-6732 147 2 inf inf NOUN ejpam-6732 147 3   PROPN ejpam-6732 147 4 sup sup NOUN ejpam-6732 147 5 m0∈z m0∈z PROPN ejpam-6732 147 6 2−m0γ 2−m0γ PROPN ejpam-6732 147 7 ( ( PUNCT ejpam-6732 147 8 m0∑ m0∑ PROPN ejpam-6732 147 9 k=−∞ k=−∞ PROPN ejpam-6732 147 10 |λk|u |λk|u PROPN ejpam-6732 147 11 ) ) PUNCT ejpam-6732 147 12 1 1 X ejpam-6732 147 13 / / SYM ejpam-6732 147 14 u u PRON ejpam-6732 147 15   PROPN ejpam-6732 147 16 . . PUNCT ejpam-6732 148 1 theorem theorem VERB ejpam-6732 148 2 14 14 NUM ejpam-6732 148 3 . . PUNCT ejpam-6732 149 1 let let VERB ejpam-6732 149 2 0 0 NUM ejpam-6732 149 3 ≤ ≤ NUM ejpam-6732 149 4 γ γ X ejpam-6732 149 5 < < X ejpam-6732 149 6 ∞ ∞ PROPN ejpam-6732 149 7 , , PUNCT ejpam-6732 149 8 0 0 NUM ejpam-6732 149 9 < < X ejpam-6732 149 10 u u X ejpam-6732 149 11 < < X ejpam-6732 149 12 ∞ ∞ PROPN ejpam-6732 149 13 , , PUNCT ejpam-6732 149 14 , , PUNCT ejpam-6732 149 15 q1 q1 PROPN ejpam-6732 149 16 ( ( PUNCT ejpam-6732 149 17 · · PUNCT ejpam-6732 149 18 ) ) PUNCT ejpam-6732 149 19 ∈ ∈ PROPN ejpam-6732 149 20 b b PROPN ejpam-6732 149 21 ( ( PUNCT ejpam-6732 149 22 rn rn NOUN ejpam-6732 149 23 ) ) PUNCT ejpam-6732 149 24 , , PUNCT ejpam-6732 149 25 and and CCONJ ejpam-6732 149 26 α α PRON ejpam-6732 149 27 ( ( PUNCT ejpam-6732 149 28 · · PUNCT ejpam-6732 149 29 ) ) PUNCT ejpam-6732 149 30 ∈ ∈ PROPN ejpam-6732 149 31 l∞ l∞ NOUN ejpam-6732 149 32 ( ( PUNCT ejpam-6732 149 33 rn rn NOUN ejpam-6732 149 34 ) ) PUNCT ejpam-6732 149 35 be be AUX ejpam-6732 149 36 log log NOUN ejpam-6732 149 37 - - PUNCT ejpam-6732 149 38 hölder hölder NOUN ejpam-6732 149 39 continuous continuous ADJ ejpam-6732 149 40 both both CCONJ ejpam-6732 149 41 at at ADP ejpam-6732 149 42 the the DET ejpam-6732 149 43 origin origin NOUN ejpam-6732 149 44 and and CCONJ ejpam-6732 149 45 infinity infinity NOUN ejpam-6732 149 46 . . PUNCT ejpam-6732 150 1 let let VERB ejpam-6732 150 2 α α PRON ejpam-6732 150 3 be be AUX ejpam-6732 150 4 such such ADJ ejpam-6732 150 5 that that PRON ejpam-6732 150 6 : : PUNCT ejpam-6732 150 7 ( ( PUNCT ejpam-6732 150 8 i i NOUN ejpam-6732 150 9 ) ) PUNCT ejpam-6732 150 10 − − PROPN ejpam-6732 150 11 n n PRON ejpam-6732 150 12 q1(0 q1(0 PROPN ejpam-6732 150 13 ) ) PUNCT ejpam-6732 151 1 − − PROPN ejpam-6732 151 2 v v INTJ ejpam-6732 151 3 − − PROPN ejpam-6732 152 1 n n NOUN ejpam-6732 152 2 s s NOUN ejpam-6732 152 3 < < X ejpam-6732 152 4 α(0 α(0 PROPN ejpam-6732 152 5 ) ) PUNCT ejpam-6732 152 6 < < X ejpam-6732 152 7 n n PROPN ejpam-6732 152 8 q′1(0 q′1(0 PROPN ejpam-6732 152 9 ) ) PUNCT ejpam-6732 153 1 − − PROPN ejpam-6732 153 2 v v ADP ejpam-6732 153 3 − − PROPN ejpam-6732 153 4 n n NOUN ejpam-6732 153 5 s s X ejpam-6732 153 6 ( ( PUNCT ejpam-6732 153 7 ii ii NOUN ejpam-6732 153 8 ) ) PUNCT ejpam-6732 153 9 − − PROPN ejpam-6732 153 10 n n CCONJ ejpam-6732 153 11 q1∞ q1∞ PROPN ejpam-6732 153 12 − − PROPN ejpam-6732 153 13 v v ADP ejpam-6732 153 14 − − PROPN ejpam-6732 154 1 n n NOUN ejpam-6732 154 2 s s X ejpam-6732 154 3 < < X ejpam-6732 154 4 α∞ α∞ PUNCT ejpam-6732 154 5 < < X ejpam-6732 154 6 n n X ejpam-6732 154 7 q′1∞ q′1∞ NOUN ejpam-6732 154 8 − − NOUN ejpam-6732 154 9 v v PART ejpam-6732 154 10 − − PROPN ejpam-6732 154 11 n n NOUN ejpam-6732 154 12 s s NOUN ejpam-6732 154 13 . . PUNCT ejpam-6732 155 1 then then ADV ejpam-6732 155 2 ∥∥∥(|z1|+ ∥∥∥(|z1|+ NOUN ejpam-6732 155 3 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 155 4 ) ) PUNCT ejpam-6732 156 1 [ [ X ejpam-6732 156 2 b b X ejpam-6732 156 3 , , PUNCT ejpam-6732 156 4 µφ µφ PROPN ejpam-6732 156 5 ] ] X ejpam-6732 156 6 m m VERB ejpam-6732 156 7 β β X ejpam-6732 156 8 f f PROPN ejpam-6732 156 9 ∥∥∥ ∥∥∥ PROPN ejpam-6732 156 10 mk̇ mk̇ PROPN ejpam-6732 156 11 α(·),u α(·),u NUM ejpam-6732 156 12 γ γ X ejpam-6732 156 13 , , PUNCT ejpam-6732 156 14 q2 q2 NOUN ejpam-6732 156 15 ( ( PUNCT ejpam-6732 156 16 · · PUNCT ejpam-6732 156 17 ) ) PUNCT ejpam-6732 156 18 ( ( PUNCT ejpam-6732 156 19 rn rn NOUN ejpam-6732 156 20 ) ) PUNCT ejpam-6732 156 21 ≤ ≤ NUM ejpam-6732 156 22 c c NOUN ejpam-6732 156 23 ∥f∥ ∥f∥ VERB ejpam-6732 156 24 hmk̇ hmk̇ PROPN ejpam-6732 156 25 α(·),u α(·),u PROPN ejpam-6732 156 26 γ γ PROPN ejpam-6732 156 27 , , PUNCT ejpam-6732 156 28 q1 q1 PROPN ejpam-6732 156 29 ( ( PUNCT ejpam-6732 156 30 · · PUNCT ejpam-6732 156 31 ) ) PUNCT ejpam-6732 156 32 ( ( PUNCT ejpam-6732 156 33 rn rn NOUN ejpam-6732 156 34 ) ) PUNCT ejpam-6732 156 35 , , PUNCT ejpam-6732 156 36 for for ADP ejpam-6732 156 37 f f PROPN ejpam-6732 156 38 ∈ ∈ PROPN ejpam-6732 156 39 hmk̇ hmk̇ PROPN ejpam-6732 156 40 α(·),u α(·),u PROPN ejpam-6732 156 41 γ γ PROPN ejpam-6732 156 42 , , PUNCT ejpam-6732 156 43 q1(·)(r q1(·)(r NOUN ejpam-6732 156 44 n n CCONJ ejpam-6732 156 45 ) ) PUNCT ejpam-6732 156 46 . . PUNCT ejpam-6732 157 1 proof proof NOUN ejpam-6732 157 2 . . PUNCT ejpam-6732 158 1 suppose suppose VERB ejpam-6732 158 2 that that SCONJ ejpam-6732 158 3 f f PROPN ejpam-6732 158 4 ∈ ∈ PROPN ejpam-6732 158 5 hmk̇ hmk̇ PROPN ejpam-6732 158 6 α(·),u α(·),u PROPN ejpam-6732 158 7 γ γ PROPN ejpam-6732 158 8 , , PUNCT ejpam-6732 158 9 q1(·)(r q1(·)(r NOUN ejpam-6732 158 10 n n NUM ejpam-6732 158 11 ) ) PUNCT ejpam-6732 158 12 . . PUNCT ejpam-6732 159 1 by by ADP ejpam-6732 159 2 using use VERB ejpam-6732 159 3 theorem theorem ADJ ejpam-6732 159 4 13 13 NUM ejpam-6732 159 5 , , PUNCT ejpam-6732 159 6 f f X ejpam-6732 159 7 = = PUNCT ejpam-6732 159 8 ∑∞ ∑∞ NOUN ejpam-6732 159 9 i=−∞ i=−∞ PRON ejpam-6732 159 10 λibi λibi NOUN ejpam-6732 159 11 converges converge VERB ejpam-6732 159 12 in in ADP ejpam-6732 159 13 s s PRON ejpam-6732 159 14 ′ ′ NUM ejpam-6732 159 15 ( ( PUNCT ejpam-6732 159 16 rn rn NOUN ejpam-6732 159 17 ) ) PUNCT ejpam-6732 159 18 , , PUNCT ejpam-6732 159 19 where where SCONJ ejpam-6732 159 20 each each DET ejpam-6732 159 21 bi bi NOUN ejpam-6732 159 22 is be AUX ejpam-6732 159 23 a a DET ejpam-6732 159 24 central central ADJ ejpam-6732 159 25 ( ( PUNCT ejpam-6732 159 26 α α X ejpam-6732 159 27 ( ( PUNCT ejpam-6732 159 28 · · PUNCT ejpam-6732 159 29 ) ) PUNCT ejpam-6732 159 30 , , PUNCT ejpam-6732 159 31 q1(·))-atom q1(·))-atom NOUN ejpam-6732 159 32 with with ADP ejpam-6732 159 33 support support NOUN ejpam-6732 159 34 contained contain VERB ejpam-6732 159 35 in in ADP ejpam-6732 159 36 bi bi NOUN ejpam-6732 159 37 and and CCONJ ejpam-6732 159 38 ∥f∥ ∥f∥ PROPN ejpam-6732 160 1 hmk̇ hmk̇ PROPN ejpam-6732 160 2 α(·),u α(·),u PROPN ejpam-6732 160 3 γ γ PROPN ejpam-6732 160 4 , , PUNCT ejpam-6732 160 5 q1 q1 PROPN ejpam-6732 160 6 ( ( PUNCT ejpam-6732 160 7 · · PUNCT ejpam-6732 160 8 ) ) PUNCT ejpam-6732 160 9 ( ( PUNCT ejpam-6732 160 10 rn rn NOUN ejpam-6732 160 11 ) ) PUNCT ejpam-6732 160 12 ≈ ≈ PROPN ejpam-6732 160 13 inf inf NOUN ejpam-6732 161 1   PROPN ejpam-6732 161 2 sup sup NOUN ejpam-6732 161 3 m0∈z m0∈z PROPN ejpam-6732 161 4 2−m0γ 2−m0γ PROPN ejpam-6732 162 1 ( ( PUNCT ejpam-6732 162 2 m0∑ m0∑ PROPN ejpam-6732 162 3 i=−∞ i=−∞ SYM ejpam-6732 162 4 |λi|u |λi|u NOUN ejpam-6732 162 5 ) ) PUNCT ejpam-6732 162 6 1 1 NUM ejpam-6732 162 7 u u NOUN ejpam-6732 162 8   PROPN ejpam-6732 162 9 . . PUNCT ejpam-6732 163 1 to to PART ejpam-6732 163 2 keep keep VERB ejpam-6732 163 3 things thing NOUN ejpam-6732 163 4 simple simple ADJ ejpam-6732 163 5 , , PUNCT ejpam-6732 163 6 we we PRON ejpam-6732 163 7 denote denote VERB ejpam-6732 163 8 λ λ X ejpam-6732 163 9 = = PUNCT ejpam-6732 164 1 supm0∈z supm0∈z ADJ ejpam-6732 164 2 2 2 NUM ejpam-6732 164 3 −m0γu −m0γu NUM ejpam-6732 164 4 ∑m0 ∑m0 NUM ejpam-6732 164 5 i=−∞ i=−∞ NOUN ejpam-6732 164 6 |λi|u |λi|u NOUN ejpam-6732 164 7 . . PUNCT ejpam-6732 164 8 by by ADP ejpam-6732 164 9 proposition proposition NOUN ejpam-6732 164 10 10 10 NUM ejpam-6732 164 11 , , PUNCT ejpam-6732 164 12 we we PRON ejpam-6732 164 13 have have VERB ejpam-6732 164 14 ∥∥∥(|z1|+ ∥∥∥(|z1|+ NOUN ejpam-6732 164 15 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 164 16 ) ) PUNCT ejpam-6732 165 1 [ [ X ejpam-6732 165 2 b b X ejpam-6732 165 3 , , PUNCT ejpam-6732 165 4 µφ µφ PROPN ejpam-6732 165 5 ] ] X ejpam-6732 165 6 m m VERB ejpam-6732 165 7 β β X ejpam-6732 165 8 f f PROPN ejpam-6732 165 9 ∥∥∥u ∥∥∥u PROPN ejpam-6732 165 10 mk̇ mk̇ PROPN ejpam-6732 165 11 α(·),u α(·),u NUM ejpam-6732 165 12 γ γ X ejpam-6732 165 13 , , PUNCT ejpam-6732 165 14 q2 q2 NOUN ejpam-6732 165 15 ( ( PUNCT ejpam-6732 165 16 · · PUNCT ejpam-6732 165 17 ) ) PUNCT ejpam-6732 165 18 ( ( PUNCT ejpam-6732 165 19 rn rn PROPN ejpam-6732 165 20 ) ) PUNCT ejpam-6732 165 21 b. b. PROPN ejpam-6732 165 22 sultan sultan PROPN ejpam-6732 165 23 et et PROPN ejpam-6732 165 24 al al PROPN ejpam-6732 165 25 . . PUNCT ejpam-6732 165 26 / / SYM ejpam-6732 165 27 eur eur PROPN ejpam-6732 165 28 . . PUNCT ejpam-6732 166 1 j. j. PROPN ejpam-6732 166 2 pure pure PROPN ejpam-6732 166 3 appl appl PROPN ejpam-6732 166 4 . . PROPN ejpam-6732 166 5 math math PROPN ejpam-6732 166 6 , , PUNCT ejpam-6732 166 7 18 18 NUM ejpam-6732 166 8 ( ( PUNCT ejpam-6732 166 9 4 4 NUM ejpam-6732 166 10 ) ) PUNCT ejpam-6732 166 11 ( ( PUNCT ejpam-6732 166 12 2025 2025 NUM ejpam-6732 166 13 ) ) PUNCT ejpam-6732 166 14 , , PUNCT ejpam-6732 166 15 6732 6732 NUM ejpam-6732 166 16 8 8 NUM ejpam-6732 166 17 of of ADP ejpam-6732 166 18 20 20 NUM ejpam-6732 166 19 ≈ ≈ PROPN ejpam-6732 166 20 max max PROPN ejpam-6732 166 21 { { PUNCT ejpam-6732 166 22 sup sup NOUN ejpam-6732 166 23 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 166 24 2−m0γu 2−m0γu NUM ejpam-6732 166 25 ( ( PUNCT ejpam-6732 166 26 m0∑ m0∑ PROPN ejpam-6732 166 27 k=−∞ k=−∞ PROPN ejpam-6732 166 28 2kα(0)u 2kα(0)u NUM ejpam-6732 167 1 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 167 2 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 167 3 ) ) PUNCT ejpam-6732 168 1 [ [ X ejpam-6732 168 2 b b X ejpam-6732 168 3 , , PUNCT ejpam-6732 168 4 µφ µφ PROPN ejpam-6732 168 5 ] ] X ejpam-6732 168 6 m m VERB ejpam-6732 168 7 β β X ejpam-6732 168 8 f f PROPN ejpam-6732 168 9 ) ) PUNCT ejpam-6732 168 10 χk χk PROPN ejpam-6732 168 11 ∥∥∥u ∥∥∥u PROPN ejpam-6732 168 12 q2 q2 PROPN ejpam-6732 168 13 ( ( PUNCT ejpam-6732 168 14 · · PUNCT ejpam-6732 168 15 ) ) PUNCT ejpam-6732 168 16 ) ) PUNCT ejpam-6732 168 17 , , PUNCT ejpam-6732 168 18 sup sup NOUN ejpam-6732 168 19 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 168 20 2−m0γu 2−m0γu NUM ejpam-6732 168 21 ( ( PUNCT ejpam-6732 168 22 −1∑ −1∑ PROPN ejpam-6732 168 23 k=−∞ k=−∞ PROPN ejpam-6732 168 24 2kα(0)u 2kα(0)u NUM ejpam-6732 169 1 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 169 2 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 169 3 ) ) PUNCT ejpam-6732 170 1 [ [ X ejpam-6732 170 2 b b X ejpam-6732 170 3 , , PUNCT ejpam-6732 170 4 µφ µφ PROPN ejpam-6732 170 5 ] ] X ejpam-6732 170 6 m m VERB ejpam-6732 170 7 β β X ejpam-6732 170 8 f f PROPN ejpam-6732 170 9 ) ) PUNCT ejpam-6732 170 10 χk χk PROPN ejpam-6732 170 11 ∥∥∥u ∥∥∥u PROPN ejpam-6732 170 12 q2 q2 PROPN ejpam-6732 170 13 ( ( PUNCT ejpam-6732 170 14 · · PUNCT ejpam-6732 170 15 ) ) PUNCT ejpam-6732 171 1 + + CCONJ ejpam-6732 171 2 m0∑ m0∑ PROPN ejpam-6732 171 3 k=0 k=0 PROPN ejpam-6732 171 4 2kα∞u 2kα∞u NUM ejpam-6732 171 5 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 171 6 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 171 7 ) ) PUNCT ejpam-6732 172 1 [ [ X ejpam-6732 172 2 b b X ejpam-6732 172 3 , , PUNCT ejpam-6732 172 4 µφ µφ PROPN ejpam-6732 172 5 ] ] X ejpam-6732 172 6 m m VERB ejpam-6732 172 7 β β X ejpam-6732 172 8 f f PROPN ejpam-6732 172 9 ) ) PUNCT ejpam-6732 172 10 χk χk PROPN ejpam-6732 172 11 ∥∥∥u ∥∥∥u PROPN ejpam-6732 172 12 q2 q2 PROPN ejpam-6732 172 13 ( ( PUNCT ejpam-6732 172 14 · · PUNCT ejpam-6732 172 15 ) ) PUNCT ejpam-6732 172 16 ) ) PUNCT ejpam-6732 172 17 } } PUNCT ejpam-6732 172 18 ≲ ≲ PROPN ejpam-6732 172 19 max{i max{i VERB ejpam-6732 172 20 , , PUNCT ejpam-6732 172 21 ii ii PROPN ejpam-6732 172 22 + + CCONJ ejpam-6732 172 23 iii iii NOUN ejpam-6732 172 24 } } PUNCT ejpam-6732 172 25 . . PUNCT ejpam-6732 173 1 we we PRON ejpam-6732 173 2 will will AUX ejpam-6732 173 3 find find VERB ejpam-6732 173 4 the the DET ejpam-6732 173 5 estimated estimate VERB ejpam-6732 173 6 for for ADP ejpam-6732 173 7 i i PROPN ejpam-6732 173 8 and and CCONJ ejpam-6732 173 9 iii iii NOUN ejpam-6732 173 10 and and CCONJ ejpam-6732 173 11 estimate estimate NOUN ejpam-6732 173 12 of of ADP ejpam-6732 173 13 ii ii PROPN ejpam-6732 173 14 can can AUX ejpam-6732 173 15 be be AUX ejpam-6732 173 16 obtained obtain VERB ejpam-6732 173 17 similarly similarly ADV ejpam-6732 173 18 . . PUNCT ejpam-6732 174 1 we we PRON ejpam-6732 174 2 just just ADV ejpam-6732 174 3 need need VERB ejpam-6732 174 4 to to PART ejpam-6732 174 5 demonstrate demonstrate VERB ejpam-6732 174 6 that that SCONJ ejpam-6732 174 7 there there PRON ejpam-6732 174 8 is be VERB ejpam-6732 174 9 a a DET ejpam-6732 174 10 positive positive ADJ ejpam-6732 174 11 constant constant ADJ ejpam-6732 174 12 c c NOUN ejpam-6732 174 13 such such ADJ ejpam-6732 174 14 that that SCONJ ejpam-6732 174 15 i i PROPN ejpam-6732 174 16 , , PUNCT ejpam-6732 174 17 ii ii PROPN ejpam-6732 174 18 , , PUNCT ejpam-6732 174 19 iii iii X ejpam-6732 174 20 ≤ ≤ NOUN ejpam-6732 174 21 cλ cλ VERB ejpam-6732 174 22 in in ADP ejpam-6732 174 23 order order NOUN ejpam-6732 174 24 to to PART ejpam-6732 174 25 finish finish VERB ejpam-6732 174 26 our our PRON ejpam-6732 174 27 proof proof NOUN ejpam-6732 174 28 . . PUNCT ejpam-6732 175 1 firstly firstly ADV ejpam-6732 175 2 , , PUNCT ejpam-6732 175 3 we we PRON ejpam-6732 175 4 will will AUX ejpam-6732 175 5 find find VERB ejpam-6732 175 6 the the DET ejpam-6732 175 7 estimate estimate NOUN ejpam-6732 175 8 of of ADP ejpam-6732 175 9 i i PRON ejpam-6732 175 10 : : PUNCT ejpam-6732 176 1 i i PRON ejpam-6732 176 2 = = NOUN ejpam-6732 176 3 sup sup NOUN ejpam-6732 176 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 176 5 2−m0γu 2−m0γu NUM ejpam-6732 177 1 ( ( PUNCT ejpam-6732 177 2 m0∑ m0∑ PROPN ejpam-6732 177 3 k=−∞ k=−∞ PROPN ejpam-6732 177 4 2kα(0)u 2kα(0)u NUM ejpam-6732 178 1 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 178 2 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 178 3 ) ) PUNCT ejpam-6732 179 1 [ [ X ejpam-6732 179 2 b b X ejpam-6732 179 3 , , PUNCT ejpam-6732 179 4 µφ µφ PROPN ejpam-6732 179 5 ] ] X ejpam-6732 179 6 m m VERB ejpam-6732 179 7 β β X ejpam-6732 179 8 f f PROPN ejpam-6732 179 9 ) ) PUNCT ejpam-6732 179 10 χk χk PROPN ejpam-6732 179 11 ∥∥∥u ∥∥∥u PROPN ejpam-6732 179 12 q2 q2 PROPN ejpam-6732 179 13 ( ( PUNCT ejpam-6732 179 14 · · PUNCT ejpam-6732 179 15 ) ) PUNCT ejpam-6732 179 16 ) ) PUNCT ejpam-6732 180 1 ≲ ≲ PROPN ejpam-6732 180 2 sup sup NOUN ejpam-6732 180 3 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 181 1 2−m0γu 2−m0γu NUM ejpam-6732 181 2 m0∑ m0∑ PROPN ejpam-6732 181 3 k=−∞ k=−∞ PROPN ejpam-6732 182 1 2kα(0)u 2kα(0)u NUM ejpam-6732 183 1 ( ( PUNCT ejpam-6732 183 2 ∞∑ ∞∑ NUM ejpam-6732 183 3 i i PROPN ejpam-6732 183 4 = = PROPN ejpam-6732 183 5 k k X ejpam-6732 183 6 |λi| |λi| NOUN ejpam-6732 183 7 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 183 8 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 183 9 ) ) PUNCT ejpam-6732 184 1 [ [ X ejpam-6732 184 2 b b X ejpam-6732 184 3 , , PUNCT ejpam-6732 184 4 µφ µφ PROPN ejpam-6732 184 5 ] ] X ejpam-6732 184 6 m m VERB ejpam-6732 184 7 β β X ejpam-6732 184 8 bi bi NOUN ejpam-6732 184 9 ) ) PUNCT ejpam-6732 184 10 χk χk PROPN ejpam-6732 184 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 184 12 q2 q2 NOUN ejpam-6732 184 13 ( ( PUNCT ejpam-6732 184 14 · · PUNCT ejpam-6732 184 15 ) ) PUNCT ejpam-6732 184 16 ) ) PUNCT ejpam-6732 184 17 u u NOUN ejpam-6732 184 18 + + NOUN ejpam-6732 184 19 sup sup PROPN ejpam-6732 184 20 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 184 21 2−m0γu 2−m0γu NUM ejpam-6732 184 22 m0∑ m0∑ PROPN ejpam-6732 184 23 k=−∞ k=−∞ PROPN ejpam-6732 184 24 2kα(0)u 2kα(0)u NUM ejpam-6732 184 25 ( ( PUNCT ejpam-6732 184 26 k−1∑ k−1∑ PROPN ejpam-6732 184 27 i=−∞ i=−∞ NUM ejpam-6732 184 28 |λi| |λi| NOUN ejpam-6732 184 29 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 184 30 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 184 31 ) ) PUNCT ejpam-6732 185 1 [ [ X ejpam-6732 185 2 b b X ejpam-6732 185 3 , , PUNCT ejpam-6732 185 4 µφ µφ PROPN ejpam-6732 185 5 ] ] X ejpam-6732 185 6 m m VERB ejpam-6732 185 7 β β X ejpam-6732 185 8 bi bi NOUN ejpam-6732 185 9 ) ) PUNCT ejpam-6732 185 10 χk χk PROPN ejpam-6732 185 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 185 12 q2 q2 NOUN ejpam-6732 185 13 ( ( PUNCT ejpam-6732 185 14 · · PUNCT ejpam-6732 185 15 ) ) PUNCT ejpam-6732 185 16 ) ) PUNCT ejpam-6732 185 17 u u NOUN ejpam-6732 185 18 : : PUNCT ejpam-6732 185 19 = = PROPN ejpam-6732 185 20 i1 i1 PROPN ejpam-6732 185 21 + + CCONJ ejpam-6732 185 22 i2 i2 PROPN ejpam-6732 185 23 . . PUNCT ejpam-6732 185 24 let let VERB ejpam-6732 185 25 k k PROPN ejpam-6732 185 26 ∈ ∈ PROPN ejpam-6732 185 27 z z PROPN ejpam-6732 186 1 and and CCONJ ejpam-6732 186 2 i i PRON ejpam-6732 186 3 ≤ ≤ X ejpam-6732 186 4 k k PROPN ejpam-6732 186 5 and and CCONJ ejpam-6732 186 6 a.e a.e PROPN ejpam-6732 186 7 . . PROPN ejpam-6732 186 8 z1 z1 PROPN ejpam-6732 186 9 ∈ ∈ PROPN ejpam-6732 186 10 fk fk INTJ ejpam-6732 186 11 , , PUNCT ejpam-6732 186 12 z2 z2 PROPN ejpam-6732 186 13 ∈ ∈ PROPN ejpam-6732 186 14 fi fi NOUN ejpam-6732 186 15 , , PUNCT ejpam-6732 186 16 it it PRON ejpam-6732 186 17 is be AUX ejpam-6732 186 18 easy easy ADJ ejpam-6732 186 19 to to PART ejpam-6732 186 20 check check VERB ejpam-6732 186 21 that that DET ejpam-6732 186 22 |z1 |z1 PROPN ejpam-6732 187 1 − − PROPN ejpam-6732 187 2 z2| z2| PROPN ejpam-6732 187 3 ≈ ≈ NUM ejpam-6732 187 4 |z1| |z1| NOUN ejpam-6732 187 5 ≈ ≈ PROPN ejpam-6732 187 6 2k 2k NUM ejpam-6732 187 7 , , PUNCT ejpam-6732 187 8 ∣∣∣([b ∣∣∣([b PROPN ejpam-6732 187 9 , , PUNCT ejpam-6732 187 10 µφ µφ ADP ejpam-6732 187 11 ] ] X ejpam-6732 187 12 m m VERB ejpam-6732 187 13 β β NOUN ejpam-6732 187 14 bi bi NOUN ejpam-6732 187 15 ) ) PUNCT ejpam-6732 187 16 ( ( PUNCT ejpam-6732 187 17 z1 z1 NOUN ejpam-6732 187 18 ) ) PUNCT ejpam-6732 187 19 ∣∣∣ ∣∣∣ ADJ ejpam-6732 187 20 ≤ ≤ PROPN ejpam-6732 187 21   X ejpam-6732 187 22 |z1|∫ |z1|∫ NOUN ejpam-6732 188 1 o o X ejpam-6732 188 2 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ PROPN ejpam-6732 188 3 ∫ ∫ PROPN ejpam-6732 188 4 |z1−z2|≤t |z1−z2|≤t PROPN ejpam-6732 188 5 φ(z1 φ(z1 NOUN ejpam-6732 188 6 − − PROPN ejpam-6732 188 7 z2 z2 PROPN ejpam-6732 188 8 ) ) PUNCT ejpam-6732 189 1 [ [ X ejpam-6732 189 2 b(z1)− b(z1)− VERB ejpam-6732 189 3 b(z2 b(z2 NOUN ejpam-6732 189 4 ) ) PUNCT ejpam-6732 189 5 ] ] PUNCT ejpam-6732 190 1 m m VERB ejpam-6732 190 2 |z1 |z1 NOUN ejpam-6732 190 3 − − PROPN ejpam-6732 190 4 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 190 5 ) ) PUNCT ejpam-6732 190 6 bi(z2)dz2 bi(z2)dz2 NOUN ejpam-6732 190 7 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ NOUN ejpam-6732 190 8 2 2 NUM ejpam-6732 190 9 dt dt NOUN ejpam-6732 190 10 t3 t3 PROPN ejpam-6732 190 11   PROPN ejpam-6732 190 12 1/2 1/2 NUM ejpam-6732 190 13 + + NUM ejpam-6732 190 14   NOUN ejpam-6732 190 15 ∞∫ ∞∫ NOUN ejpam-6732 190 16 |z1| |z1| NOUN ejpam-6732 190 17 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ PROPN ejpam-6732 190 18 ∫ ∫ PROPN ejpam-6732 190 19 |z1−z2|≤t |z1−z2|≤t PROPN ejpam-6732 190 20 φ(z1 φ(z1 NOUN ejpam-6732 190 21 − − PROPN ejpam-6732 190 22 z2 z2 PROPN ejpam-6732 190 23 ) ) PUNCT ejpam-6732 191 1 [ [ X ejpam-6732 191 2 b(z1)− b(z1)− VERB ejpam-6732 191 3 b(z2 b(z2 NOUN ejpam-6732 191 4 ) ) PUNCT ejpam-6732 191 5 ] ] PUNCT ejpam-6732 192 1 m m VERB ejpam-6732 192 2 |z1 |z1 NOUN ejpam-6732 192 3 − − PROPN ejpam-6732 192 4 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 192 5 ) ) PUNCT ejpam-6732 192 6 bi(z2)dz2 bi(z2)dz2 NOUN ejpam-6732 192 7 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ NOUN ejpam-6732 192 8 2 2 NUM ejpam-6732 192 9 dt dt NOUN ejpam-6732 192 10 t3 t3 PROPN ejpam-6732 192 11   PROPN ejpam-6732 192 12 1/2 1/2 NUM ejpam-6732 192 13 = = NOUN ejpam-6732 192 14 : : PUNCT ejpam-6732 192 15 i11 i11 ADJ ejpam-6732 192 16 + + CCONJ ejpam-6732 192 17 i12 i12 ADJ ejpam-6732 192 18 . . PUNCT ejpam-6732 193 1 mean mean ADJ ejpam-6732 193 2 value value NOUN ejpam-6732 193 3 theorem theorem VERB ejpam-6732 193 4 yields yield NOUN ejpam-6732 193 5 ∣∣∣∣ ∣∣∣∣ NOUN ejpam-6732 193 6 1 1 NUM ejpam-6732 193 7 |z1 |z1 NOUN ejpam-6732 193 8 − − PROPN ejpam-6732 193 9 z2|2 z2|2 NUM ejpam-6732 193 10 − − PROPN ejpam-6732 193 11 1 1 NUM ejpam-6732 193 12 |z1|2 |z1|2 PROPN ejpam-6732 193 13 ∣∣∣∣ ∣∣∣∣ NOUN ejpam-6732 193 14 ≤ ≤ NOUN ejpam-6732 193 15 |z2| |z2| VERB ejpam-6732 193 16 |z1 |z1 PROPN ejpam-6732 193 17 − − PROPN ejpam-6732 193 18 z2|3 z2|3 NOUN ejpam-6732 193 19 . . PUNCT ejpam-6732 194 1 ( ( PUNCT ejpam-6732 194 2 2.1 2.1 NUM ejpam-6732 194 3 ) ) PUNCT ejpam-6732 194 4 b. b. PROPN ejpam-6732 194 5 sultan sultan PROPN ejpam-6732 194 6 et et PROPN ejpam-6732 194 7 al al PROPN ejpam-6732 194 8 . . PUNCT ejpam-6732 194 9 / / SYM ejpam-6732 194 10 eur eur PROPN ejpam-6732 194 11 . . PUNCT ejpam-6732 195 1 j. j. PROPN ejpam-6732 195 2 pure pure PROPN ejpam-6732 195 3 appl appl PROPN ejpam-6732 195 4 . . PROPN ejpam-6732 195 5 math math PROPN ejpam-6732 195 6 , , PUNCT ejpam-6732 195 7 18 18 NUM ejpam-6732 195 8 ( ( PUNCT ejpam-6732 195 9 4 4 NUM ejpam-6732 195 10 ) ) PUNCT ejpam-6732 195 11 ( ( PUNCT ejpam-6732 195 12 2025 2025 NUM ejpam-6732 195 13 ) ) PUNCT ejpam-6732 195 14 , , PUNCT ejpam-6732 195 15 6732 6732 NUM ejpam-6732 195 16 9 9 NUM ejpam-6732 195 17 of of ADP ejpam-6732 195 18 20 20 NUM ejpam-6732 195 19 for for ADP ejpam-6732 195 20 i11 i11 ADJ ejpam-6732 195 21 , , PUNCT ejpam-6732 195 22 we we PRON ejpam-6732 195 23 get get VERB ejpam-6732 195 24 i11 i11 ADJ ejpam-6732 195 25 ≤ ≤ NUM ejpam-6732 195 26 ∫ ∫ PROPN ejpam-6732 195 27 rn rn PROPN ejpam-6732 195 28 |φ(z1 |φ(z1 PROPN ejpam-6732 195 29 − − PROPN ejpam-6732 195 30 z2)| z2)| PROPN ejpam-6732 196 1 [ [ X ejpam-6732 196 2 b(z1)− b(z1)− VERB ejpam-6732 196 3 b(z2 b(z2 NOUN ejpam-6732 196 4 ) ) PUNCT ejpam-6732 196 5 ] ] PUNCT ejpam-6732 197 1 m m AUX ejpam-6732 197 2 |z1 |z1 NOUN ejpam-6732 197 3 − − PROPN ejpam-6732 197 4 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 197 5 ) ) PUNCT ejpam-6732 197 6 |bi(z2)| |bi(z2)| NOUN ejpam-6732 197 7   X ejpam-6732 197 8 |z1|∫ |z1|∫ NUM ejpam-6732 197 9 |z1−z2| |z1−z2| PROPN ejpam-6732 198 1 dt dt X ejpam-6732 198 2 t3 t3 PROPN ejpam-6732 198 3   PROPN ejpam-6732 198 4 1/2 1/2 NUM ejpam-6732 198 5 dz2 dz2 NOUN ejpam-6732 198 6 ≤ ≤ NUM ejpam-6732 198 7 ∫ ∫ PROPN ejpam-6732 198 8 rn rn PROPN ejpam-6732 198 9 |φ(z1 |φ(z1 PROPN ejpam-6732 198 10 − − PROPN ejpam-6732 198 11 z2)| z2)| PROPN ejpam-6732 199 1 [ [ X ejpam-6732 199 2 b(z1)− b(z1)− VERB ejpam-6732 199 3 b(z2 b(z2 NOUN ejpam-6732 199 4 ) ) PUNCT ejpam-6732 199 5 ] ] PUNCT ejpam-6732 200 1 m m AUX ejpam-6732 200 2 |z1 |z1 NOUN ejpam-6732 200 3 − − PROPN ejpam-6732 200 4 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 200 5 ) ) PUNCT ejpam-6732 200 6 |bi(z2)| |bi(z2)| NOUN ejpam-6732 200 7 ∣∣∣∣ ∣∣∣∣ NOUN ejpam-6732 200 8 1 1 NUM ejpam-6732 200 9 |z1 |z1 NOUN ejpam-6732 200 10 − − PROPN ejpam-6732 200 11 z2|2 z2|2 NUM ejpam-6732 200 12 − − PROPN ejpam-6732 200 13 1 1 NUM ejpam-6732 200 14 |z1|2 |z1|2 PROPN ejpam-6732 200 15 ∣∣∣∣1/2 ∣∣∣∣1/2 ADJ ejpam-6732 200 16 dz2 dz2 NOUN ejpam-6732 200 17 ≤ ≤ NUM ejpam-6732 200 18 ∫ ∫ PROPN ejpam-6732 200 19 rn rn PROPN ejpam-6732 200 20 |φ(z1 |φ(z1 PROPN ejpam-6732 200 21 − − PROPN ejpam-6732 200 22 z2)| z2)| PROPN ejpam-6732 201 1 [ [ X ejpam-6732 201 2 b(z1)− b(z1)− VERB ejpam-6732 201 3 b(z2 b(z2 NOUN ejpam-6732 201 4 ) ) PUNCT ejpam-6732 201 5 ] ] PUNCT ejpam-6732 202 1 m m VERB ejpam-6732 202 2 |z1 |z1 NOUN ejpam-6732 202 3 − − PROPN ejpam-6732 202 4 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 202 5 ) ) PUNCT ejpam-6732 202 6 |bi(z2)| |bi(z2)| NOUN ejpam-6732 202 7 ∣∣∣∣ ∣∣∣∣ NOUN ejpam-6732 202 8 |z2 |z2 ADJ ejpam-6732 202 9 |z1 |z1 NOUN ejpam-6732 202 10 − − ADP ejpam-6732 202 11 z2|3 z2|3 NOUN ejpam-6732 202 12 ∣∣∣∣1/2 ∣∣∣∣1/2 VERB ejpam-6732 202 13 dz2 dz2 NOUN ejpam-6732 202 14 ≤ ≤ NOUN ejpam-6732 203 1 2l/2 2l/2 NUM ejpam-6732 204 1 |z1|n+ |z1|n+ PROPN ejpam-6732 204 2 1 1 NUM ejpam-6732 204 3 2 2 NUM ejpam-6732 204 4 . . PUNCT ejpam-6732 204 5 |z1|−β(z1 |z1|−β(z1 PROPN ejpam-6732 204 6 ) ) PUNCT ejpam-6732 204 7 ∫ ∫ PROPN ejpam-6732 204 8 fi fi NOUN ejpam-6732 204 9 |φ(z1 |φ(z1 PROPN ejpam-6732 204 10 − − PROPN ejpam-6732 204 11 z2)| z2)| PROPN ejpam-6732 205 1 [ [ X ejpam-6732 205 2 b(z1)− b(z1)− VERB ejpam-6732 205 3 b(z2 b(z2 NOUN ejpam-6732 205 4 ) ) PUNCT ejpam-6732 205 5 ] ] PUNCT ejpam-6732 206 1 m m VERB ejpam-6732 206 2 |bi(z2)| |bi(z2)| NOUN ejpam-6732 206 3 dz2 dz2 NOUN ejpam-6732 206 4 ≤2(i−k)/22−kn ≤2(i−k)/22−kn NOUN ejpam-6732 206 5 |z1|β(z1 |z1|β(z1 NOUN ejpam-6732 206 6 ) ) PUNCT ejpam-6732 206 7 ∥bi∥q1 ∥bi∥q1 NOUN ejpam-6732 206 8 ( ( PUNCT ejpam-6732 206 9 · · PUNCT ejpam-6732 206 10 ) ) PUNCT ejpam-6732 206 11 ∥φ(z1 ∥φ(z1 NOUN ejpam-6732 206 12 − − NOUN ejpam-6732 206 13 · · PUNCT ejpam-6732 206 14 ) ) PUNCT ejpam-6732 206 15 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 206 16 ( ( PUNCT ejpam-6732 206 17 · · PUNCT ejpam-6732 206 18 ) ) PUNCT ejpam-6732 206 19 . . PUNCT ejpam-6732 207 1 ≤2(i−k)/22−kn ≤2(i−k)/22−kn PROPN ejpam-6732 207 2 |z1|β(z1 |z1|β(z1 NUM ejpam-6732 207 3 ) ) PUNCT ejpam-6732 207 4 { { PUNCT ejpam-6732 207 5 |b(z1)− |b(z1)− NOUN ejpam-6732 207 6 bbi bbi VERB ejpam-6732 207 7 | | ADV ejpam-6732 207 8 m m VERB ejpam-6732 207 9 ∫ ∫ PROPN ejpam-6732 207 10 fi fi NOUN ejpam-6732 207 11 |φ(z1 |φ(z1 PROPN ejpam-6732 207 12 − − PROPN ejpam-6732 207 13 z2)| z2)| PROPN ejpam-6732 207 14 |bi(z2)| |bi(z2)| NOUN ejpam-6732 207 15 dz2 dz2 NOUN ejpam-6732 207 16 + + CCONJ ejpam-6732 207 17 ∫ ∫ PROPN ejpam-6732 207 18 fi fi NOUN ejpam-6732 207 19 |b(z2)− |b(z2)− VERB ejpam-6732 207 20 bbi bbi VERB ejpam-6732 207 21 |m |m NOUN ejpam-6732 207 22 |φ(z1 |φ(z1 ADJ ejpam-6732 207 23 − − PROPN ejpam-6732 207 24 z2)| z2)| NOUN ejpam-6732 207 25 |bi(z2)| |bi(z2)| NOUN ejpam-6732 207 26 dz2 dz2 NOUN ejpam-6732 207 27 } } PUNCT ejpam-6732 207 28 ≤2(i−k)/22−kn ≤2(i−k)/22−kn NOUN ejpam-6732 207 29 |z1|β(z1 |z1|β(z1 NOUN ejpam-6732 207 30 ) ) PUNCT ejpam-6732 207 31 ∥bi(z2)∥q1 ∥bi(z2)∥q1 NOUN ejpam-6732 207 32 ( ( PUNCT ejpam-6732 207 33 · · PUNCT ejpam-6732 207 34 ) ) PUNCT ejpam-6732 207 35 ( ( PUNCT ejpam-6732 207 36 |b(z1)− |b(z1)− NOUN ejpam-6732 207 37 bbi bbi VERB ejpam-6732 207 38 | | ADV ejpam-6732 207 39 m m VERB ejpam-6732 207 40 ∥φ(z1 ∥φ(z1 ADJ ejpam-6732 207 41 − − NOUN ejpam-6732 207 42 · · PUNCT ejpam-6732 207 43 ) ) PUNCT ejpam-6732 207 44 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 207 45 ( ( PUNCT ejpam-6732 207 46 · · PUNCT ejpam-6732 207 47 ) ) PUNCT ejpam-6732 208 1 + + NUM ejpam-6732 208 2 ∥(b(·)− ∥(b(·)− NUM ejpam-6732 208 3 bbi bbi ADJ ejpam-6732 208 4 ) ) PUNCT ejpam-6732 208 5 m(φ(z1 m(φ(z1 NOUN ejpam-6732 208 6 − − PROPN ejpam-6732 208 7 · · PUNCT ejpam-6732 208 8 ) ) PUNCT ejpam-6732 208 9 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 208 10 ( ( PUNCT ejpam-6732 208 11 · · PUNCT ejpam-6732 208 12 ) ) PUNCT ejpam-6732 208 13 ) ) PUNCT ejpam-6732 208 14 . . PUNCT ejpam-6732 209 1 similarly similarly ADV ejpam-6732 209 2 , , PUNCT ejpam-6732 209 3 we we PRON ejpam-6732 209 4 can can AUX ejpam-6732 209 5 consider consider VERB ejpam-6732 209 6 i12 i12 PROPN ejpam-6732 209 7 , , PUNCT ejpam-6732 209 8 we we PRON ejpam-6732 209 9 have have VERB ejpam-6732 209 10 i12 i12 VERB ejpam-6732 209 11 ≤ ≤ NUM ejpam-6732 209 12 ∫ ∫ PROPN ejpam-6732 209 13 rn rn PROPN ejpam-6732 209 14 |φ(z |φ(z PROPN ejpam-6732 209 15 − − PROPN ejpam-6732 209 16 1− 1− NUM ejpam-6732 209 17 z2)| z2)| PROPN ejpam-6732 209 18 |z1 |z1 PROPN ejpam-6732 209 19 − − PROPN ejpam-6732 209 20 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 209 21 ) ) PUNCT ejpam-6732 210 1 |bi(z2)| |bi(z2)| NOUN ejpam-6732 210 2   NUM ejpam-6732 210 3 ∞∫ ∞∫ PROPN ejpam-6732 210 4 |z1| |z1| NOUN ejpam-6732 210 5 dt dt PROPN ejpam-6732 210 6 t3 t3 PROPN ejpam-6732 210 7   PROPN ejpam-6732 210 8 1/2 1/2 NUM ejpam-6732 210 9 dz2 dz2 NOUN ejpam-6732 210 10 ≤ ≤ NUM ejpam-6732 210 11 ∫ ∫ PROPN ejpam-6732 210 12 rn rn PROPN ejpam-6732 210 13 |φ(z1 |φ(z1 PROPN ejpam-6732 210 14 − − PROPN ejpam-6732 210 15 z2)| z2)| PROPN ejpam-6732 210 16 |z1 |z1 PROPN ejpam-6732 210 17 − − PROPN ejpam-6732 210 18 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 210 19 ) ) PUNCT ejpam-6732 211 1 |bi(z2)| |bi(z2)| NOUN ejpam-6732 211 2 dz2 dz2 NOUN ejpam-6732 211 3 ≤|z1|−n ≤|z1|−n PROPN ejpam-6732 211 4 |z1|β(z1 |z1|β(z1 PROPN ejpam-6732 211 5 ) ) PUNCT ejpam-6732 211 6 ∫ ∫ PROPN ejpam-6732 211 7 fi fi NOUN ejpam-6732 211 8 |φ(z1 |φ(z1 PROPN ejpam-6732 211 9 − − PROPN ejpam-6732 211 10 z2)| z2)| PROPN ejpam-6732 211 11 |bi(z2)| |bi(z2)| NOUN ejpam-6732 211 12 dz2 dz2 NOUN ejpam-6732 211 13 ≤2−kn ≤2−kn X ejpam-6732 211 14 |z1|β(z1 |z1|β(z1 NOUN ejpam-6732 211 15 ) ) PUNCT ejpam-6732 211 16 ∥bi(z2)∥q1 ∥bi(z2)∥q1 NOUN ejpam-6732 211 17 ( ( PUNCT ejpam-6732 211 18 · · PUNCT ejpam-6732 211 19 ) ) PUNCT ejpam-6732 211 20 { { PUNCT ejpam-6732 212 1 |b(z1)− |b(z1)− NOUN ejpam-6732 212 2 bbi bbi VERB ejpam-6732 212 3 | | ADV ejpam-6732 212 4 m m VERB ejpam-6732 212 5 ∥φ(z1 ∥φ(z1 ADJ ejpam-6732 212 6 − − NOUN ejpam-6732 212 7 · · PUNCT ejpam-6732 212 8 ) ) PUNCT ejpam-6732 212 9 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 212 10 ( ( PUNCT ejpam-6732 212 11 · · PUNCT ejpam-6732 212 12 ) ) PUNCT ejpam-6732 213 1 + + NUM ejpam-6732 213 2 ∥(b(·)− ∥(b(·)− NUM ejpam-6732 213 3 bbi bbi VERB ejpam-6732 213 4 ) ) PUNCT ejpam-6732 213 5 m m PROPN ejpam-6732 213 6 ( ( PUNCT ejpam-6732 213 7 φ(z1 φ(z1 NOUN ejpam-6732 213 8 − − NOUN ejpam-6732 213 9 · · PUNCT ejpam-6732 213 10 ) ) PUNCT ejpam-6732 213 11 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 213 12 ( ( PUNCT ejpam-6732 213 13 · · PUNCT ejpam-6732 213 14 ) ) PUNCT ejpam-6732 213 15 } } PUNCT ejpam-6732 213 16 . . PUNCT ejpam-6732 214 1 we we PRON ejpam-6732 214 2 define define VERB ejpam-6732 214 3 q1 q1 PROPN ejpam-6732 214 4 ( ( PUNCT ejpam-6732 214 5 · · PUNCT ejpam-6732 214 6 ) ) PUNCT ejpam-6732 214 7 by by ADP ejpam-6732 214 8 the the DET ejpam-6732 214 9 relation relation NOUN ejpam-6732 214 10 1 1 NUM ejpam-6732 214 11 q′1(x q′1(x NOUN ejpam-6732 214 12 ) ) PUNCT ejpam-6732 214 13 = = SYM ejpam-6732 215 1 1 1 NUM ejpam-6732 215 2 q1(x q1(x NOUN ejpam-6732 215 3 ) ) PUNCT ejpam-6732 216 1 + + CCONJ ejpam-6732 216 2 1 1 NUM ejpam-6732 216 3 s s NOUN ejpam-6732 216 4 . . PUNCT ejpam-6732 217 1 by by ADP ejpam-6732 217 2 using use VERB ejpam-6732 217 3 lemma lemma PROPN ejpam-6732 217 4 ( ( PUNCT ejpam-6732 217 5 7 7 NUM ejpam-6732 217 6 ) ) PUNCT ejpam-6732 217 7 and and CCONJ ejpam-6732 217 8 generalized generalized ADJ ejpam-6732 217 9 hölder hölder NOUN ejpam-6732 217 10 ’s ’s PART ejpam-6732 217 11 inequality inequality NOUN ejpam-6732 217 12 we we PRON ejpam-6732 217 13 have have VERB ejpam-6732 217 14 ∥φ(z1 ∥φ(z1 ADJ ejpam-6732 217 15 − − NOUN ejpam-6732 217 16 · · SYM ejpam-6732 217 17 ) ) PUNCT ejpam-6732 217 18 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 217 19 ( ( PUNCT ejpam-6732 217 20 · · PUNCT ejpam-6732 217 21 ) ) PUNCT ejpam-6732 217 22 ≤∥φ(z1 ≤∥φ(z1 NOUN ejpam-6732 217 23 − − NOUN ejpam-6732 217 24 · · SYM ejpam-6732 217 25 ) ) PUNCT ejpam-6732 217 26 χi(·)∥ls(sn−1 χi(·)∥ls(sn−1 ADJ ejpam-6732 217 27 ) ) PUNCT ejpam-6732 217 28 ∥χi(·)∥q1 ∥χi(·)∥q1 NOUN ejpam-6732 217 29 ( ( PUNCT ejpam-6732 217 30 · · PUNCT ejpam-6732 217 31 ) ) PUNCT ejpam-6732 218 1 b. b. PROPN ejpam-6732 218 2 sultan sultan PROPN ejpam-6732 218 3 et et PROPN ejpam-6732 218 4 al al PROPN ejpam-6732 218 5 . . PUNCT ejpam-6732 218 6 / / SYM ejpam-6732 218 7 eur eur PROPN ejpam-6732 218 8 . . PUNCT ejpam-6732 219 1 j. j. PROPN ejpam-6732 219 2 pure pure PROPN ejpam-6732 219 3 appl appl PROPN ejpam-6732 219 4 . . PROPN ejpam-6732 219 5 math math PROPN ejpam-6732 219 6 , , PUNCT ejpam-6732 219 7 18 18 NUM ejpam-6732 219 8 ( ( PUNCT ejpam-6732 219 9 4 4 NUM ejpam-6732 219 10 ) ) PUNCT ejpam-6732 219 11 ( ( PUNCT ejpam-6732 219 12 2025 2025 NUM ejpam-6732 219 13 ) ) PUNCT ejpam-6732 219 14 , , PUNCT ejpam-6732 219 15 6732 6732 NUM ejpam-6732 219 16 10 10 NUM ejpam-6732 219 17 of of ADP ejpam-6732 219 18 20 20 NUM ejpam-6732 219 19 ≤2−iv ≤2−iv PROPN ejpam-6732 219 20   PROPN ejpam-6732 219 21 ∫ ∫ PROPN ejpam-6732 219 22 2l−1<|z2|<2i 2l−1<|z2|<2i NUM ejpam-6732 219 23 |φ(z1 |φ(z1 ADJ ejpam-6732 219 24 − − PROPN ejpam-6732 219 25 z2)|s|z2|svdz2 z2)|s|z2|svdz2 PROPN ejpam-6732 219 26   PROPN ejpam-6732 219 27 1 1 NUM ejpam-6732 219 28 / / SYM ejpam-6732 219 29 s s PART ejpam-6732 219 30 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 219 31 ( ( PUNCT ejpam-6732 219 32 · · PUNCT ejpam-6732 219 33 ) ) PUNCT ejpam-6732 219 34 ≤2−iv2k(v+ ≤2−iv2k(v+ PROPN ejpam-6732 219 35 n n PRON ejpam-6732 219 36 s s NOUN ejpam-6732 219 37 ) ) PUNCT ejpam-6732 219 38 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 219 39 ) ) PUNCT ejpam-6732 219 40 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 219 41 ( ( PUNCT ejpam-6732 219 42 · · PUNCT ejpam-6732 219 43 ) ) PUNCT ejpam-6732 219 44 . . PUNCT ejpam-6732 220 1 similarly similarly ADV ejpam-6732 220 2 , , PUNCT ejpam-6732 220 3 by by ADP ejpam-6732 220 4 using use VERB ejpam-6732 220 5 lemma lemma PROPN ejpam-6732 220 6 ( ( PUNCT ejpam-6732 220 7 6 6 NUM ejpam-6732 220 8 ) ) PUNCT ejpam-6732 220 9 we we PRON ejpam-6732 220 10 have have VERB ejpam-6732 220 11 ∥(b(·)− ∥(b(·)− NOUN ejpam-6732 220 12 bbi bbi ADJ ejpam-6732 220 13 ) ) PUNCT ejpam-6732 220 14 m(φ(z1 m(φ(z1 NOUN ejpam-6732 220 15 − − PROPN ejpam-6732 220 16 · · PUNCT ejpam-6732 220 17 ) ) PUNCT ejpam-6732 220 18 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 220 19 ( ( PUNCT ejpam-6732 220 20 · · PUNCT ejpam-6732 220 21 ) ) PUNCT ejpam-6732 220 22 ≤∥φ(z1 ≤∥φ(z1 NOUN ejpam-6732 220 23 − − PROPN ejpam-6732 220 24 · · PUNCT ejpam-6732 220 25 ) ) PUNCT ejpam-6732 220 26 χi(·)∥s χi(·)∥s X ejpam-6732 220 27 ∥(b(·)− ∥(b(·)− NUM ejpam-6732 220 28 bbi bbi ADJ ejpam-6732 220 29 ) ) PUNCT ejpam-6732 220 30 mχi(·)∥q mχi(·)∥q VERB ejpam-6732 220 31 ( ( PUNCT ejpam-6732 220 32 · · PUNCT ejpam-6732 220 33 ) ) PUNCT ejpam-6732 220 34 ≤c ≤c PROPN ejpam-6732 220 35 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 220 36 ∥χbi∥q ∥χbi∥q PROPN ejpam-6732 220 37 ( ( PUNCT ejpam-6732 220 38 · · PUNCT ejpam-6732 220 39 ) ) PUNCT ejpam-6732 220 40 ∥φ(z1 ∥φ(z1 NOUN ejpam-6732 220 41 − − NOUN ejpam-6732 220 42 · · PUNCT ejpam-6732 220 43 ) ) PUNCT ejpam-6732 220 44 χi(·)∥s χi(·)∥s PROPN ejpam-6732 220 45 ≤c ≤c PROPN ejpam-6732 220 46 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 220 47 2−iv2k(v+ 2−iv2k(v+ NUM ejpam-6732 220 48 n n SYM ejpam-6732 220 49 s s PART ejpam-6732 220 50 ) ) PUNCT ejpam-6732 220 51 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 220 52 ) ) PUNCT ejpam-6732 220 53 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 220 54 ( ( PUNCT ejpam-6732 220 55 · · PUNCT ejpam-6732 220 56 ) ) PUNCT ejpam-6732 220 57 . . PUNCT ejpam-6732 221 1 it it PRON ejpam-6732 221 2 is be AUX ejpam-6732 221 3 known know VERB ejpam-6732 221 4 , , PUNCT ejpam-6732 221 5 see see VERB ejpam-6732 221 6 e.g. e.g. ADV ejpam-6732 221 7 [ [ X ejpam-6732 221 8 36 36 NUM ejpam-6732 221 9 ] ] PUNCT ejpam-6732 221 10 that that SCONJ ejpam-6732 221 11 iβ iβ ADP ejpam-6732 221 12 ( ( PUNCT ejpam-6732 221 13 · · PUNCT ejpam-6732 221 14 ) ) PUNCT ejpam-6732 221 15 ( ( PUNCT ejpam-6732 221 16 ( ( PUNCT ejpam-6732 221 17 b(z1)− b(z1)− VERB ejpam-6732 221 18 bbi bbi ADJ ejpam-6732 221 19 ) ) PUNCT ejpam-6732 221 20 mχbk mχbk NOUN ejpam-6732 221 21 ) ) PUNCT ejpam-6732 221 22 ( ( PUNCT ejpam-6732 221 23 z1 z1 PROPN ejpam-6732 221 24 ) ) PUNCT ejpam-6732 221 25 ≥ ≥ NOUN ejpam-6732 221 26 iβ(·)(χbk iβ(·)(χbk PROPN ejpam-6732 221 27 ) ) PUNCT ejpam-6732 221 28 ( ( PUNCT ejpam-6732 221 29 z1).(χbk z1).(χbk PROPN ejpam-6732 221 30 ) ) PUNCT ejpam-6732 221 31 ( ( PUNCT ejpam-6732 221 32 z1 z1 NOUN ejpam-6732 221 33 ) ) PUNCT ejpam-6732 221 34 = = SYM ejpam-6732 222 1 ∫ ∫ PROPN ejpam-6732 222 2 bk bk PROPN ejpam-6732 222 3 |b(z1)− |b(z1)− PROPN ejpam-6732 222 4 bbi bbi VERB ejpam-6732 222 5 | | ADV ejpam-6732 222 6 m m VERB ejpam-6732 222 7 |z1 |z1 NOUN ejpam-6732 222 8 − − PROPN ejpam-6732 223 1 z2|β(z1)−n z2|β(z1)−n ADV ejpam-6732 223 2 dz2.χbk dz2.χbk PROPN ejpam-6732 223 3 ( ( PUNCT ejpam-6732 223 4 z1 z1 PROPN ejpam-6732 223 5 ) ) PUNCT ejpam-6732 223 6 ≥ ≥ NOUN ejpam-6732 223 7 c c PROPN ejpam-6732 223 8 |b(z1)− |b(z1)− NOUN ejpam-6732 223 9 bbi bbi VERB ejpam-6732 223 10 | | ADV ejpam-6732 223 11 m m NOUN ejpam-6732 223 12 |z1|β(z1 |z1|β(z1 ADJ ejpam-6732 223 13 ) ) PUNCT ejpam-6732 223 14 .χbk .χbk PUNCT ejpam-6732 224 1 ( ( PUNCT ejpam-6732 224 2 z1 z1 PROPN ejpam-6732 224 3 ) ) PUNCT ejpam-6732 224 4 ≥ ≥ NOUN ejpam-6732 224 5 c c PROPN ejpam-6732 224 6 |b(z1)− |b(z1)− NOUN ejpam-6732 224 7 bbi bbi VERB ejpam-6732 224 8 | | ADV ejpam-6732 224 9 m m NOUN ejpam-6732 224 10 |z1|β(z1 |z1|β(z1 ADJ ejpam-6732 224 11 ) ) PUNCT ejpam-6732 224 12 .χk(z1 .χk(z1 NOUN ejpam-6732 224 13 ) ) PUNCT ejpam-6732 224 14 . . PUNCT ejpam-6732 225 1 consequently consequently ADV ejpam-6732 225 2 , , PUNCT ejpam-6732 225 3 by by ADP ejpam-6732 225 4 using use VERB ejpam-6732 225 5 weighted weight VERB ejpam-6732 225 6 sobolev sobolev NOUN ejpam-6732 225 7 estimates estimate NOUN ejpam-6732 225 8 [ [ X ejpam-6732 225 9 37 37 NUM ejpam-6732 225 10 ] ] PUNCT ejpam-6732 225 11 we we PRON ejpam-6732 225 12 have∥∥∥(b(z1)− have∥∥∥(b(z1)− VERB ejpam-6732 225 13 bbi bbi VERB ejpam-6732 225 14 ) ) PUNCT ejpam-6732 225 15 m m PROPN ejpam-6732 225 16 |z1|β(z1 |z1|β(z1 ADJ ejpam-6732 225 17 ) ) PUNCT ejpam-6732 225 18 χk(z1)(1 χk(z1)(1 NOUN ejpam-6732 226 1 + + CCONJ ejpam-6732 226 2 |z1|)−λ(z1 |z1|)−λ(z1 NOUN ejpam-6732 226 3 ) ) PUNCT ejpam-6732 226 4 ∥∥∥ ∥∥∥ PROPN ejpam-6732 226 5 q2 q2 NOUN ejpam-6732 226 6 ( ( PUNCT ejpam-6732 226 7 · · PUNCT ejpam-6732 226 8 ) ) PUNCT ejpam-6732 226 9 ≤ ≤ NOUN ejpam-6732 226 10 ∥∥∥(1 ∥∥∥(1 PUNCT ejpam-6732 226 11 + + CCONJ ejpam-6732 226 12 |z1|)−λ(z1)(iβ(·)((b(z1)− |z1|)−λ(z1)(iβ(·)((b(z1)− NOUN ejpam-6732 226 13 bbi bbi VERB ejpam-6732 226 14 ) ) PUNCT ejpam-6732 226 15 mχbk mχbk NOUN ejpam-6732 226 16 ) ) PUNCT ejpam-6732 226 17 ( ( PUNCT ejpam-6732 226 18 z1 z1 NOUN ejpam-6732 226 19 ) ) PUNCT ejpam-6732 226 20 ) ) PUNCT ejpam-6732 226 21 ∥∥∥ ∥∥∥ PROPN ejpam-6732 226 22 q2 q2 NOUN ejpam-6732 226 23 ( ( PUNCT ejpam-6732 226 24 · · PUNCT ejpam-6732 226 25 ) ) PUNCT ejpam-6732 226 26 ≤ ≤ NUM ejpam-6732 226 27 ∥(b(z1)− ∥(b(z1)− ADJ ejpam-6732 226 28 bbi bbi VERB ejpam-6732 226 29 ) ) PUNCT ejpam-6732 226 30 mχbk mχbk NOUN ejpam-6732 226 31 ) ) PUNCT ejpam-6732 226 32 ( ( PUNCT ejpam-6732 226 33 z1)∥q1 z1)∥q1 PROPN ejpam-6732 226 34 ( ( PUNCT ejpam-6732 226 35 · · PUNCT ejpam-6732 226 36 ) ) PUNCT ejpam-6732 226 37 . . PUNCT ejpam-6732 227 1 thus thus ADV ejpam-6732 227 2 we we PRON ejpam-6732 227 3 have∥∥∥χk(1 have∥∥∥χk(1 NOUN ejpam-6732 227 4 + + X ejpam-6732 227 5 |z1|)−λ(z1 |z1|)−λ(z1 NOUN ejpam-6732 227 6 ) ) PUNCT ejpam-6732 228 1 [ [ X ejpam-6732 228 2 b b X ejpam-6732 228 3 , , PUNCT ejpam-6732 228 4 µφ µφ PROPN ejpam-6732 228 5 ] ] X ejpam-6732 228 6 m m VERB ejpam-6732 228 7 β β X ejpam-6732 228 8 bi bi PROPN ejpam-6732 228 9 ∥∥∥ ∥∥∥ PROPN ejpam-6732 228 10 q2 q2 PROPN ejpam-6732 228 11 ( ( PUNCT ejpam-6732 228 12 · · PUNCT ejpam-6732 228 13 ) ) PUNCT ejpam-6732 228 14 ≤ ≤ NOUN ejpam-6732 228 15 c2−kn c2−kn PROPN ejpam-6732 228 16 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 228 17 ( ( PUNCT ejpam-6732 228 18 · · PUNCT ejpam-6732 228 19 ) ) PUNCT ejpam-6732 228 20 { { PUNCT ejpam-6732 228 21 ∥∥∥(b(z1)− ∥∥∥(b(z1)− NOUN ejpam-6732 228 22 bbi bbi PROPN ejpam-6732 228 23 ) ) PUNCT ejpam-6732 228 24 m m PROPN ejpam-6732 228 25 |z1|β(z1 |z1|β(z1 ADJ ejpam-6732 228 26 ) ) PUNCT ejpam-6732 228 27 χk(z1)(1 χk(z1)(1 NOUN ejpam-6732 228 28 + + CCONJ ejpam-6732 228 29 |z1|)−λ(z1 |z1|)−λ(z1 NOUN ejpam-6732 228 30 ) ) PUNCT ejpam-6732 228 31 ∥∥∥ ∥∥∥ PROPN ejpam-6732 228 32 q2 q2 NOUN ejpam-6732 228 33 ( ( PUNCT ejpam-6732 228 34 · · PUNCT ejpam-6732 228 35 ) ) PUNCT ejpam-6732 228 36 2−iv2k(v+ 2−iv2k(v+ NUM ejpam-6732 229 1 n n SYM ejpam-6732 229 2 s s NOUN ejpam-6732 229 3 ) ) PUNCT ejpam-6732 229 4 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 229 5 ) ) PUNCT ejpam-6732 229 6 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 229 7 ( ( PUNCT ejpam-6732 229 8 · · PUNCT ejpam-6732 229 9 ) ) PUNCT ejpam-6732 230 1 + + CCONJ ejpam-6732 230 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 230 3 2−iv2k(v+ 2−iv2k(v+ NUM ejpam-6732 230 4 n n SYM ejpam-6732 230 5 s s PART ejpam-6732 230 6 ) ) PUNCT ejpam-6732 230 7 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 230 8 ) ) PUNCT ejpam-6732 230 9 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 230 10 ( ( PUNCT ejpam-6732 230 11 · · PUNCT ejpam-6732 230 12 ) ) PUNCT ejpam-6732 230 13 ∥∥∥|z1|β(z1 ∥∥∥|z1|β(z1 NUM ejpam-6732 230 14 ) ) PUNCT ejpam-6732 230 15 χk(z1)(1 χk(z1)(1 NOUN ejpam-6732 230 16 + + CCONJ ejpam-6732 230 17 |z1|)−λ(z1 |z1|)−λ(z1 NOUN ejpam-6732 230 18 ) ) PUNCT ejpam-6732 230 19 ∥∥∥ ∥∥∥ PROPN ejpam-6732 230 20 q2 q2 NOUN ejpam-6732 230 21 ( ( PUNCT ejpam-6732 230 22 · · PUNCT ejpam-6732 230 23 ) ) PUNCT ejpam-6732 230 24 } } PUNCT ejpam-6732 230 25 ≤ ≤ NUM ejpam-6732 230 26 c2−kn c2−kn PROPN ejpam-6732 230 27 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 230 28 ( ( PUNCT ejpam-6732 230 29 · · PUNCT ejpam-6732 230 30 ) ) PUNCT ejpam-6732 230 31 { { PUNCT ejpam-6732 230 32 ( ( PUNCT ejpam-6732 230 33 k k NOUN ejpam-6732 230 34 − − PROPN ejpam-6732 230 35 i)m i)m NOUN ejpam-6732 230 36 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 230 37 ∥χbk ∥χbk NUM ejpam-6732 230 38 ∥q1 ∥q1 NOUN ejpam-6732 230 39 ( ( PUNCT ejpam-6732 230 40 · · PUNCT ejpam-6732 230 41 ) ) PUNCT ejpam-6732 230 42 2 2 NUM ejpam-6732 230 43 −iv2k(v+ −iv2k(v+ PROPN ejpam-6732 230 44 n n PART ejpam-6732 230 45 s s PART ejpam-6732 230 46 ) ) PUNCT ejpam-6732 230 47 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 230 48 ) ) PUNCT ejpam-6732 230 49 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 230 50 ( ( PUNCT ejpam-6732 230 51 · · PUNCT ejpam-6732 230 52 ) ) PUNCT ejpam-6732 230 53 + + CCONJ ejpam-6732 230 54 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 230 55 2−iv2k(v+ 2−iv2k(v+ NUM ejpam-6732 230 56 n n SYM ejpam-6732 230 57 s s PART ejpam-6732 230 58 ) ) PUNCT ejpam-6732 230 59 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 230 60 ) ) PUNCT ejpam-6732 230 61 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 230 62 ( ( PUNCT ejpam-6732 230 63 · · PUNCT ejpam-6732 230 64 ) ) PUNCT ejpam-6732 230 65 ∥χbk ∥χbk NUM ejpam-6732 230 66 ∥q1 ∥q1 NOUN ejpam-6732 230 67 ( ( PUNCT ejpam-6732 230 68 · · PUNCT ejpam-6732 230 69 ) ) PUNCT ejpam-6732 230 70 } } PUNCT ejpam-6732 230 71 ≤ ≤ NUM ejpam-6732 230 72 c2−kn c2−kn PROPN ejpam-6732 230 73 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 230 74 ( ( PUNCT ejpam-6732 230 75 · · PUNCT ejpam-6732 230 76 ) ) PUNCT ejpam-6732 230 77 ( ( PUNCT ejpam-6732 230 78 k k NOUN ejpam-6732 230 79 − − PROPN ejpam-6732 230 80 i)m i)m NOUN ejpam-6732 230 81 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 230 82 ∥χbk ∥χbk NUM ejpam-6732 230 83 ∥q1 ∥q1 NOUN ejpam-6732 230 84 ( ( PUNCT ejpam-6732 230 85 · · PUNCT ejpam-6732 230 86 ) ) PUNCT ejpam-6732 230 87 2 2 NUM ejpam-6732 230 88 −iv2k(v+ −iv2k(v+ PROPN ejpam-6732 230 89 n n PART ejpam-6732 230 90 s s PART ejpam-6732 230 91 ) ) PUNCT ejpam-6732 230 92 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 230 93 ) ) PUNCT ejpam-6732 230 94 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 230 95 ( ( PUNCT ejpam-6732 230 96 · · PUNCT ejpam-6732 230 97 ) ) PUNCT ejpam-6732 230 98 ≤ ≤ NUM ejpam-6732 231 1 c(k c(k PROPN ejpam-6732 231 2 − − NOUN ejpam-6732 231 3 i)m i)m NOUN ejpam-6732 231 4 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 ADJ ejpam-6732 231 5 ) ) PUNCT ejpam-6732 231 6 ∥f∥ ∥f∥ PROPN ejpam-6732 231 7 m m PROPN ejpam-6732 231 8 bmo bmo NOUN ejpam-6732 231 9 2−kn2−iv2k(v+ 2−kn2−iv2k(v+ NUM ejpam-6732 231 10 n n X ejpam-6732 231 11 s s PART ejpam-6732 231 12 ) ) PUNCT ejpam-6732 231 13 ∥χbk ∥χbk NUM ejpam-6732 231 14 ∥q1 ∥q1 NOUN ejpam-6732 231 15 ( ( PUNCT ejpam-6732 231 16 · · PUNCT ejpam-6732 231 17 ) ) PUNCT ejpam-6732 231 18 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 231 19 ( ( PUNCT ejpam-6732 231 20 · · PUNCT ejpam-6732 231 21 ) ) PUNCT ejpam-6732 231 22 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 231 23 ( ( PUNCT ejpam-6732 231 24 · · PUNCT ejpam-6732 231 25 ) ) PUNCT ejpam-6732 231 26 . . PUNCT ejpam-6732 232 1 b. b. PROPN ejpam-6732 232 2 sultan sultan PROPN ejpam-6732 232 3 et et PROPN ejpam-6732 232 4 al al PROPN ejpam-6732 232 5 . . PUNCT ejpam-6732 232 6 / / SYM ejpam-6732 232 7 eur eur PROPN ejpam-6732 232 8 . . PUNCT ejpam-6732 233 1 j. j. PROPN ejpam-6732 233 2 pure pure PROPN ejpam-6732 233 3 appl appl PROPN ejpam-6732 233 4 . . PROPN ejpam-6732 233 5 math math PROPN ejpam-6732 233 6 , , PUNCT ejpam-6732 233 7 18 18 NUM ejpam-6732 233 8 ( ( PUNCT ejpam-6732 233 9 4 4 NUM ejpam-6732 233 10 ) ) PUNCT ejpam-6732 233 11 ( ( PUNCT ejpam-6732 233 12 2025 2025 NUM ejpam-6732 233 13 ) ) PUNCT ejpam-6732 233 14 , , PUNCT ejpam-6732 233 15 6732 6732 NUM ejpam-6732 233 16 11 11 NUM ejpam-6732 233 17 of of ADP ejpam-6732 233 18 20 20 NUM ejpam-6732 233 19 therefore therefore ADV ejpam-6732 233 20 , , PUNCT ejpam-6732 233 21 when when SCONJ ejpam-6732 233 22 0 0 NUM ejpam-6732 233 23 < < X ejpam-6732 233 24 u u X ejpam-6732 233 25 ≤ ≤ ADV ejpam-6732 233 26 1 1 NUM ejpam-6732 233 27 and and CCONJ ejpam-6732 233 28 v1 v1 VERB ejpam-6732 233 29 = = SYM ejpam-6732 233 30 n n CCONJ ejpam-6732 233 31 / / SYM ejpam-6732 233 32 q′1(0)− q′1(0)− PROPN ejpam-6732 233 33 v v ADP ejpam-6732 233 34 − − PROPN ejpam-6732 233 35 n n PROPN ejpam-6732 233 36 s s NOUN ejpam-6732 233 37 − − PROPN ejpam-6732 233 38 α(0 α(0 PROPN ejpam-6732 233 39 ) ) PUNCT ejpam-6732 233 40 , , PUNCT ejpam-6732 233 41 we we PRON ejpam-6732 233 42 get get VERB ejpam-6732 233 43 i1 i1 NOUN ejpam-6732 233 44 = = PUNCT ejpam-6732 233 45 sup sup NOUN ejpam-6732 233 46 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 234 1 2−m0γu 2−m0γu NUM ejpam-6732 234 2 m0∑ m0∑ PROPN ejpam-6732 234 3 k=−∞ k=−∞ PROPN ejpam-6732 235 1 2kα(0)u 2kα(0)u NUM ejpam-6732 236 1 ( ( PUNCT ejpam-6732 236 2 ∞∑ ∞∑ NUM ejpam-6732 236 3 i i PROPN ejpam-6732 236 4 = = PROPN ejpam-6732 236 5 k k X ejpam-6732 236 6 |λi| |λi| NOUN ejpam-6732 236 7 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 236 8 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 236 9 ) ) PUNCT ejpam-6732 237 1 [ [ X ejpam-6732 237 2 b b X ejpam-6732 237 3 , , PUNCT ejpam-6732 237 4 µφ µφ PROPN ejpam-6732 237 5 ] ] X ejpam-6732 237 6 m m VERB ejpam-6732 237 7 β β X ejpam-6732 237 8 bi bi NOUN ejpam-6732 237 9 ) ) PUNCT ejpam-6732 237 10 χk χk PROPN ejpam-6732 237 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 237 12 q2 q2 NOUN ejpam-6732 237 13 ( ( PUNCT ejpam-6732 237 14 · · PUNCT ejpam-6732 237 15 ) ) PUNCT ejpam-6732 237 16 ) ) PUNCT ejpam-6732 238 1 u u PROPN ejpam-6732 238 2 ≲ ≲ PROPN ejpam-6732 238 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 238 4 sup sup NOUN ejpam-6732 238 5 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 239 1 2−m0γu 2−m0γu NUM ejpam-6732 239 2 m0∑ m0∑ PROPN ejpam-6732 239 3 k=−∞ k=−∞ PROPN ejpam-6732 239 4 2α(0)ku 2α(0)ku NUM ejpam-6732 239 5 ( ( PUNCT ejpam-6732 239 6 ∞∑ ∞∑ NUM ejpam-6732 239 7 i i PROPN ejpam-6732 239 8 = = PROPN ejpam-6732 239 9 k k NOUN ejpam-6732 239 10 |λi| |λi| NOUN ejpam-6732 239 11 2−kn2−iv2k(v+ 2−kn2−iv2k(v+ NUM ejpam-6732 239 12 n n NOUN ejpam-6732 239 13 s s PART ejpam-6732 239 14 ) ) PUNCT ejpam-6732 239 15 ∥χbk ∥χbk NUM ejpam-6732 239 16 ∥q1 ∥q1 NOUN ejpam-6732 239 17 ( ( PUNCT ejpam-6732 239 18 · · PUNCT ejpam-6732 239 19 ) ) PUNCT ejpam-6732 239 20 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 239 21 ( ( PUNCT ejpam-6732 239 22 · · PUNCT ejpam-6732 239 23 ) ) PUNCT ejpam-6732 239 24 ( ( PUNCT ejpam-6732 239 25 k k NOUN ejpam-6732 239 26 − − PROPN ejpam-6732 239 27 i)m2−αii i)m2−αii NOUN ejpam-6732 239 28 ) ) PUNCT ejpam-6732 239 29 u u PROPN ejpam-6732 239 30 ≲ ≲ PROPN ejpam-6732 239 31 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 239 32 sup sup NOUN ejpam-6732 239 33 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 240 1 2−m0γu 2−m0γu NUM ejpam-6732 240 2 m0∑ m0∑ PROPN ejpam-6732 240 3 k=−∞ k=−∞ PROPN ejpam-6732 241 1 2kα(0)u 2kα(0)u NUM ejpam-6732 241 2 × × NOUN ejpam-6732 241 3 ( ( PUNCT ejpam-6732 241 4 −1∑ −1∑ PROPN ejpam-6732 241 5 i i PROPN ejpam-6732 241 6 = = PROPN ejpam-6732 241 7 k k X ejpam-6732 241 8 |λi|u |λi|u NOUN ejpam-6732 241 9 2−α(0)iu2u(i−k)(n 2−α(0)iu2u(i−k)(n NUM ejpam-6732 241 10 / / SYM ejpam-6732 241 11 q′1(0)−v−n q′1(0)−v−n PROPN ejpam-6732 241 12 s s PART ejpam-6732 241 13 ) ) PUNCT ejpam-6732 241 14 ( ( PUNCT ejpam-6732 241 15 k k PROPN ejpam-6732 241 16 − − PROPN ejpam-6732 242 1 i)mu i)mu PROPN ejpam-6732 242 2 + + CCONJ ejpam-6732 242 3 ∞∑ ∞∑ PROPN ejpam-6732 242 4 i=0 i=0 ADJ ejpam-6732 242 5 |λi|u |λi|u ADP ejpam-6732 242 6 2−α∞iu2−ui(n 2−α∞iu2−ui(n NUM ejpam-6732 242 7 / / SYM ejpam-6732 242 8 q1∞+v+n q1∞+v+n PROPN ejpam-6732 242 9 s s PART ejpam-6732 242 10 ) ) PUNCT ejpam-6732 242 11 + + ADJ ejpam-6732 242 12 uk(n uk(n NUM ejpam-6732 242 13 / / SYM ejpam-6732 242 14 q1(0)+v+n q1(0)+v+n NOUN ejpam-6732 242 15 s s PART ejpam-6732 242 16 ) ) PUNCT ejpam-6732 242 17 ( ( PUNCT ejpam-6732 242 18 k k PROPN ejpam-6732 242 19 − − PROPN ejpam-6732 242 20 i)mu i)mu PROPN ejpam-6732 242 21 ) ) PUNCT ejpam-6732 243 1 ≲ ≲ PROPN ejpam-6732 243 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 243 3 sup sup NOUN ejpam-6732 243 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 244 1 2−m0γu 2−m0γu NUM ejpam-6732 244 2 m0∑ m0∑ PROPN ejpam-6732 244 3 k=−∞ k=−∞ PUNCT ejpam-6732 245 1 −1∑ −1∑ PROPN ejpam-6732 245 2 i i PROPN ejpam-6732 245 3 = = PROPN ejpam-6732 245 4 k k X ejpam-6732 245 5 |λi|u |λi|u NOUN ejpam-6732 245 6 2v1(i−k)u(k 2v1(i−k)u(k PROPN ejpam-6732 245 7 − − PUNCT ejpam-6732 246 1 i)mu i)mu NOUN ejpam-6732 246 2 + + CCONJ ejpam-6732 246 3 ∥f∥mbmo ∥f∥mbmo NUM ejpam-6732 246 4 sup sup NOUN ejpam-6732 246 5 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 247 1 2−m0γu 2−m0γu NUM ejpam-6732 247 2 m0∑ m0∑ PROPN ejpam-6732 247 3 k=−∞ k=−∞ PROPN ejpam-6732 248 1 2(α(0)+(n 2(α(0)+(n X ejpam-6732 248 2 / / SYM ejpam-6732 248 3 q1(0)+v+n q1(0)+v+n NOUN ejpam-6732 248 4 s s PART ejpam-6732 248 5 ) ) PUNCT ejpam-6732 248 6 ) ) PUNCT ejpam-6732 249 1 ku ku PROPN ejpam-6732 249 2 ∞∑ ∞∑ PROPN ejpam-6732 249 3 i=0 i=0 PROPN ejpam-6732 249 4 |λi|u |λi|u NOUN ejpam-6732 249 5 2((n 2((n NUM ejpam-6732 249 6 / / SYM ejpam-6732 249 7 q1∞+v+n q1∞+v+n PROPN ejpam-6732 249 8 s s PART ejpam-6732 249 9 ) ) PUNCT ejpam-6732 249 10 −α∞)iu(k −α∞)iu(k ADJ ejpam-6732 249 11 − − PUNCT ejpam-6732 250 1 i)mu i)mu PROPN ejpam-6732 250 2 ≲ ≲ PROPN ejpam-6732 250 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 250 4 sup sup NOUN ejpam-6732 250 5 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 250 6 2−m0γu 2−m0γu NUM ejpam-6732 250 7 −1∑ −1∑ PROPN ejpam-6732 250 8 i=−∞ i=−∞ NOUN ejpam-6732 250 9 |λi|u |λi|u NOUN ejpam-6732 250 10 i∑ i∑ PROPN ejpam-6732 250 11 k=−∞ k=−∞ NOUN ejpam-6732 250 12 2v1(i−k)u(k 2v1(i−k)u(k NUM ejpam-6732 251 1 − − PUNCT ejpam-6732 252 1 i)mu i)mu NOUN ejpam-6732 252 2 + + CCONJ ejpam-6732 252 3 ∥f∥mbmo ∥f∥mbmo NUM ejpam-6732 252 4 sup sup NOUN ejpam-6732 252 5 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 252 6 2−m0γu 2−m0γu NUM ejpam-6732 252 7 ∞∑ ∞∑ PRON ejpam-6732 252 8 i=0 i=0 PROPN ejpam-6732 252 9 i∑ i∑ PROPN ejpam-6732 252 10 j=−∞ j=−∞ NOUN ejpam-6732 252 11 |λj |λj PRON ejpam-6732 252 12 |u |u ADJ ejpam-6732 252 13 2(−ui(n 2(−ui(n NUM ejpam-6732 252 14 / / SYM ejpam-6732 252 15 q1∞+v+n q1∞+v+n NOUN ejpam-6732 252 16 s s PART ejpam-6732 252 17 + + NOUN ejpam-6732 252 18 α∞))(k α∞))(k X ejpam-6732 252 19 − − ADP ejpam-6732 252 20 i)mu i)mu PROPN ejpam-6732 252 21 ≲ ≲ PROPN ejpam-6732 252 22 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 252 23 sup sup NOUN ejpam-6732 252 24 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 253 1 2−m0γu 2−m0γu NUM ejpam-6732 253 2 m0∑ m0∑ PROPN ejpam-6732 253 3 i=−∞ i=−∞ SYM ejpam-6732 253 4 |λi|u |λi|u NOUN ejpam-6732 253 5 + + CCONJ ejpam-6732 253 6 λ λ PROPN ejpam-6732 253 7 sup sup NOUN ejpam-6732 253 8 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 253 9 2−m0γu 2−m0γu NUM ejpam-6732 254 1 ∞∑ ∞∑ DET ejpam-6732 254 2 i=0 i=0 PROPN ejpam-6732 254 3 2(−ui(n 2(−ui(n NUM ejpam-6732 254 4 / / SYM ejpam-6732 254 5 q1∞+v+n q1∞+v+n NOUN ejpam-6732 254 6 s s PART ejpam-6732 254 7 + + NOUN ejpam-6732 254 8 α∞))(k α∞))(k X ejpam-6732 254 9 − − ADP ejpam-6732 255 1 i)mu i)mu PROPN ejpam-6732 255 2 ≲ ≲ PROPN ejpam-6732 255 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 255 4 λ λ PROPN ejpam-6732 255 5 . . PUNCT ejpam-6732 256 1 now now ADV ejpam-6732 256 2 we we PRON ejpam-6732 256 3 will will AUX ejpam-6732 256 4 the the DET ejpam-6732 256 5 estimate estimate VERB ejpam-6732 256 6 for for ADP ejpam-6732 256 7 the the DET ejpam-6732 256 8 second second ADJ ejpam-6732 256 9 case case NOUN ejpam-6732 256 10 when when SCONJ ejpam-6732 256 11 1 1 NUM ejpam-6732 256 12 < < X ejpam-6732 256 13 u u X ejpam-6732 256 14 < < X ejpam-6732 256 15 ∞. ∞. PROPN ejpam-6732 256 16 let let VERB ejpam-6732 256 17 1 1 NUM ejpam-6732 256 18 u u NOUN ejpam-6732 256 19 + + NOUN ejpam-6732 256 20 1 1 NUM ejpam-6732 256 21 u′ u′ NOUN ejpam-6732 256 22 = = SYM ejpam-6732 256 23 1 1 NUM ejpam-6732 256 24 , , PUNCT ejpam-6732 256 25 we we PRON ejpam-6732 256 26 obtain obtain VERB ejpam-6732 256 27 i1 i1 NOUN ejpam-6732 256 28 = = PUNCT ejpam-6732 257 1 sup sup NOUN ejpam-6732 257 2 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 258 1 2−m0γu 2−m0γu NUM ejpam-6732 258 2 m0∑ m0∑ PROPN ejpam-6732 258 3 k=−∞ k=−∞ PROPN ejpam-6732 259 1 2kα(0)u 2kα(0)u NUM ejpam-6732 260 1 ( ( PUNCT ejpam-6732 260 2 ∞∑ ∞∑ NUM ejpam-6732 260 3 i i PROPN ejpam-6732 260 4 = = PROPN ejpam-6732 260 5 k k X ejpam-6732 260 6 |λi| |λi| NOUN ejpam-6732 260 7 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 260 8 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 260 9 ) ) PUNCT ejpam-6732 261 1 [ [ X ejpam-6732 261 2 b b X ejpam-6732 261 3 , , PUNCT ejpam-6732 261 4 µφ µφ PROPN ejpam-6732 261 5 ] ] X ejpam-6732 261 6 m m VERB ejpam-6732 261 7 β β X ejpam-6732 261 8 bi bi NOUN ejpam-6732 261 9 ) ) PUNCT ejpam-6732 261 10 χk χk PROPN ejpam-6732 261 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 261 12 q2 q2 NOUN ejpam-6732 261 13 ( ( PUNCT ejpam-6732 261 14 · · PUNCT ejpam-6732 261 15 ) ) PUNCT ejpam-6732 261 16 ) ) PUNCT ejpam-6732 262 1 u u PROPN ejpam-6732 262 2 ≲ ≲ PROPN ejpam-6732 262 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 262 4 sup sup NOUN ejpam-6732 262 5 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 263 1 2−m0γu 2−m0γu NUM ejpam-6732 263 2 m0∑ m0∑ PROPN ejpam-6732 263 3 k=−∞ k=−∞ PROPN ejpam-6732 263 4 2α(0)ku 2α(0)ku NUM ejpam-6732 263 5 ( ( PUNCT ejpam-6732 263 6 ∞∑ ∞∑ NUM ejpam-6732 263 7 i i PROPN ejpam-6732 263 8 = = PROPN ejpam-6732 263 9 k k NOUN ejpam-6732 263 10 |λi| |λi| NOUN ejpam-6732 263 11 2−kn2−iv2k(v+ 2−kn2−iv2k(v+ NUM ejpam-6732 263 12 n n NOUN ejpam-6732 263 13 s s PART ejpam-6732 263 14 ) ) PUNCT ejpam-6732 263 15 ∥χbk ∥χbk NUM ejpam-6732 263 16 ∥q1 ∥q1 NOUN ejpam-6732 263 17 ( ( PUNCT ejpam-6732 263 18 · · PUNCT ejpam-6732 263 19 ) ) PUNCT ejpam-6732 263 20 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 263 21 ( ( PUNCT ejpam-6732 263 22 · · PUNCT ejpam-6732 263 23 ) ) PUNCT ejpam-6732 263 24 ( ( PUNCT ejpam-6732 263 25 k k NOUN ejpam-6732 263 26 − − PROPN ejpam-6732 263 27 i)m2−αii i)m2−αii NOUN ejpam-6732 263 28 ) ) PUNCT ejpam-6732 263 29 u u PROPN ejpam-6732 263 30 b. b. PROPN ejpam-6732 263 31 sultan sultan PROPN ejpam-6732 263 32 et et PROPN ejpam-6732 263 33 al al PROPN ejpam-6732 263 34 . . PUNCT ejpam-6732 263 35 / / SYM ejpam-6732 263 36 eur eur PROPN ejpam-6732 263 37 . . PUNCT ejpam-6732 264 1 j. j. PROPN ejpam-6732 264 2 pure pure PROPN ejpam-6732 264 3 appl appl PROPN ejpam-6732 264 4 . . PROPN ejpam-6732 264 5 math math PROPN ejpam-6732 264 6 , , PUNCT ejpam-6732 264 7 18 18 NUM ejpam-6732 264 8 ( ( PUNCT ejpam-6732 264 9 4 4 NUM ejpam-6732 264 10 ) ) PUNCT ejpam-6732 264 11 ( ( PUNCT ejpam-6732 264 12 2025 2025 NUM ejpam-6732 264 13 ) ) PUNCT ejpam-6732 264 14 , , PUNCT ejpam-6732 264 15 6732 6732 NUM ejpam-6732 264 16 12 12 NUM ejpam-6732 264 17 of of ADP ejpam-6732 264 18 20 20 NUM ejpam-6732 264 19 ≲ ≲ PROPN ejpam-6732 264 20 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 264 21 sup sup NOUN ejpam-6732 264 22 m0<0,m0∈z m0<0,m0∈z PROPN ejpam-6732 265 1 2−m0γu 2−m0γu NUM ejpam-6732 265 2 × × NOUN ejpam-6732 265 3 m0∑ m0∑ PROPN ejpam-6732 265 4 k=−∞ k=−∞ PROPN ejpam-6732 266 1 2kα(0)u 2kα(0)u NUM ejpam-6732 266 2 ( ( PUNCT ejpam-6732 266 3 −1∑ −1∑ PROPN ejpam-6732 266 4 i i PROPN ejpam-6732 266 5 = = PROPN ejpam-6732 266 6 k k X ejpam-6732 266 7 |λi|u |λi|u NOUN ejpam-6732 266 8 2−α(0)iu2u(i−k)(n 2−α(0)iu2u(i−k)(n NUM ejpam-6732 266 9 / / SYM ejpam-6732 266 10 q′1(0)−v−n q′1(0)−v−n PROPN ejpam-6732 266 11 s s PART ejpam-6732 266 12 ) ) PUNCT ejpam-6732 266 13 ( ( PUNCT ejpam-6732 266 14 k k PROPN ejpam-6732 266 15 − − PROPN ejpam-6732 266 16 i)mu i)mu PROPN ejpam-6732 266 17 + + CCONJ ejpam-6732 266 18 ∞∑ ∞∑ PROPN ejpam-6732 266 19 i=0 i=0 ADJ ejpam-6732 266 20 |λi|u |λi|u ADP ejpam-6732 266 21 2−α∞iu2−ui(n 2−α∞iu2−ui(n NUM ejpam-6732 266 22 / / SYM ejpam-6732 266 23 q1∞+v+n q1∞+v+n PROPN ejpam-6732 266 24 s s PART ejpam-6732 266 25 ) ) PUNCT ejpam-6732 267 1 + + ADJ ejpam-6732 267 2 uk(n uk(n NUM ejpam-6732 267 3 / / SYM ejpam-6732 267 4 q1(0)+v+n q1(0)+v+n NOUN ejpam-6732 267 5 s s PART ejpam-6732 267 6 ) ) PUNCT ejpam-6732 267 7 ( ( PUNCT ejpam-6732 267 8 k k PROPN ejpam-6732 267 9 − − PROPN ejpam-6732 267 10 i)mu i)mu PROPN ejpam-6732 267 11 ) ) PUNCT ejpam-6732 268 1 ≲ ≲ PROPN ejpam-6732 268 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 268 3 sup sup NOUN ejpam-6732 268 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 269 1 2−m0γu 2−m0γu NUM ejpam-6732 269 2 m0∑ m0∑ PROPN ejpam-6732 269 3 k=−∞ k=−∞ PROPN ejpam-6732 270 1 ( ( PUNCT ejpam-6732 270 2 −1∑ −1∑ PROPN ejpam-6732 270 3 i i PROPN ejpam-6732 270 4 = = PROPN ejpam-6732 270 5 k k X ejpam-6732 270 6 |λi|u |λi|u NOUN ejpam-6732 270 7 2v1(i−k)u/2 2v1(i−k)u/2 NUM ejpam-6732 270 8 ) ) PUNCT ejpam-6732 270 9 × × NOUN ejpam-6732 270 10 ( ( PUNCT ejpam-6732 270 11 −1∑ −1∑ PROPN ejpam-6732 270 12 i i PROPN ejpam-6732 270 13 = = PROPN ejpam-6732 270 14 k k PROPN ejpam-6732 270 15 2α(0)(k−i)u′/2(k 2α(0)(k−i)u′/2(k NOUN ejpam-6732 270 16 − − PROPN ejpam-6732 270 17 i)mu′/2 i)mu′/2 NOUN ejpam-6732 270 18 ) ) PUNCT ejpam-6732 270 19 u u NOUN ejpam-6732 270 20 / / SYM ejpam-6732 270 21 u′ u′ PROPN ejpam-6732 270 22 + + CCONJ ejpam-6732 270 23 sup sup PROPN ejpam-6732 270 24 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 270 25 2−m0γu 2−m0γu NUM ejpam-6732 270 26 m0∑ m0∑ PROPN ejpam-6732 270 27 k=−∞ k=−∞ NOUN ejpam-6732 271 1 2(α(0)n 2(α(0)n NUM ejpam-6732 271 2 / / SYM ejpam-6732 271 3 q1(0)+v+n q1(0)+v+n PROPN ejpam-6732 271 4 s s PART ejpam-6732 271 5 ) ) PUNCT ejpam-6732 271 6 ku ku PROPN ejpam-6732 271 7 ( ( PUNCT ejpam-6732 271 8 ∞∑ ∞∑ NUM ejpam-6732 271 9 i=0 i=0 PROPN ejpam-6732 271 10 |λi|u |λi|u NOUN ejpam-6732 271 11 2−iu(α∞+n 2−iu(α∞+n NOUN ejpam-6732 271 12 / / SYM ejpam-6732 271 13 q1∞+v+n q1∞+v+n PROPN ejpam-6732 271 14 s s PART ejpam-6732 271 15 ) ) PUNCT ejpam-6732 271 16 u/2 u/2 NUM ejpam-6732 271 17 ) ) PUNCT ejpam-6732 271 18 × × NOUN ejpam-6732 271 19 ( ( PUNCT ejpam-6732 271 20 ∞∑ ∞∑ DET ejpam-6732 271 21 i=0 i=0 ADJ ejpam-6732 271 22 2−iu(α∞+n 2−iu(α∞+n NOUN ejpam-6732 271 23 / / SYM ejpam-6732 271 24 q1∞+v+n q1∞+v+n PROPN ejpam-6732 271 25 s s PART ejpam-6732 271 26 ) ) PUNCT ejpam-6732 271 27 u′/2(k u′/2(k PROPN ejpam-6732 271 28 − − PROPN ejpam-6732 271 29 i)mu′/2 i)mu′/2 NOUN ejpam-6732 271 30 ) ) PUNCT ejpam-6732 271 31 u u NOUN ejpam-6732 271 32 / / SYM ejpam-6732 271 33 u′ u′ PROPN ejpam-6732 271 34 ≲ ≲ PROPN ejpam-6732 271 35 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 271 36 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 271 37 sup sup NOUN ejpam-6732 271 38 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 272 1 2−m0γu 2−m0γu NUM ejpam-6732 272 2 m0∑ m0∑ PROPN ejpam-6732 272 3 k=−∞ k=−∞ PROPN ejpam-6732 273 1 ( ( PUNCT ejpam-6732 273 2 −1∑ −1∑ PROPN ejpam-6732 273 3 i i PROPN ejpam-6732 273 4 = = PROPN ejpam-6732 273 5 k k X ejpam-6732 273 6 |λi|u |λi|u NOUN ejpam-6732 273 7 2v1(i−k)u/2 2v1(i−k)u/2 NUM ejpam-6732 273 8 ) ) PUNCT ejpam-6732 274 1 + + CCONJ ejpam-6732 274 2 ∥f∥mbmo ∥f∥mbmo NUM ejpam-6732 274 3 sup sup NOUN ejpam-6732 274 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 275 1 2−m0γu 2−m0γu NUM ejpam-6732 275 2 m0∑ m0∑ PROPN ejpam-6732 275 3 k=−∞ k=−∞ NOUN ejpam-6732 276 1 2(α(0)n 2(α(0)n NUM ejpam-6732 276 2 / / SYM ejpam-6732 276 3 q1(0)+v+n q1(0)+v+n PROPN ejpam-6732 276 4 s s PART ejpam-6732 276 5 ) ) PUNCT ejpam-6732 276 6 ku ku PROPN ejpam-6732 276 7 ( ( PUNCT ejpam-6732 276 8 ∞∑ ∞∑ NUM ejpam-6732 276 9 i=0 i=0 PROPN ejpam-6732 276 10 |λi|u |λi|u NOUN ejpam-6732 276 11 2−iu(α∞+n 2−iu(α∞+n NOUN ejpam-6732 276 12 / / SYM ejpam-6732 276 13 q1∞+v+n q1∞+v+n PROPN ejpam-6732 276 14 s s PART ejpam-6732 276 15 ) ) PUNCT ejpam-6732 276 16 u/2 u/2 NUM ejpam-6732 276 17 ) ) PUNCT ejpam-6732 277 1 ≲ ≲ PROPN ejpam-6732 277 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 277 3 sup sup NOUN ejpam-6732 277 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 277 5 2−m0γu 2−m0γu NUM ejpam-6732 277 6 −1∑ −1∑ PROPN ejpam-6732 277 7 i=−∞ i=−∞ NOUN ejpam-6732 277 8 |λi|u |λi|u NOUN ejpam-6732 277 9 i∑ i∑ PROPN ejpam-6732 277 10 k=−∞ k=−∞ X ejpam-6732 277 11 2v1(i−k)u/2 2v1(i−k)u/2 NUM ejpam-6732 278 1 + + CCONJ ejpam-6732 278 2 ∥f∥mbmo ∥f∥mbmo NUM ejpam-6732 278 3 sup sup NOUN ejpam-6732 278 4 m0<0,m0∈z m0<0,m0∈z PROPN ejpam-6732 278 5 2−m0γu 2−m0γu NUM ejpam-6732 278 6 ( ( PUNCT ejpam-6732 278 7 ∞∑ ∞∑ NUM ejpam-6732 278 8 i=0 i=0 ADJ ejpam-6732 278 9 |λi|u |λi|u NOUN ejpam-6732 278 10 2−iu(α∞+n 2−iu(α∞+n NOUN ejpam-6732 278 11 / / SYM ejpam-6732 278 12 q1∞+v+n q1∞+v+n PROPN ejpam-6732 278 13 s s PART ejpam-6732 278 14 ) ) PUNCT ejpam-6732 278 15 u/2 u/2 NUM ejpam-6732 278 16 ) ) PUNCT ejpam-6732 279 1 ≲ ≲ PROPN ejpam-6732 279 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 279 3 sup sup NOUN ejpam-6732 279 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 279 5 2−m0γu 2−m0γu NUM ejpam-6732 279 6 −1∑ −1∑ PROPN ejpam-6732 279 7 i=−∞ i=−∞ NOUN ejpam-6732 279 8 |λi|u |λi|u NOUN ejpam-6732 279 9 i∑ i∑ PROPN ejpam-6732 279 10 k=−∞ k=−∞ X ejpam-6732 279 11 2v1(i−k)u/2 2v1(i−k)u/2 NUM ejpam-6732 280 1 + + CCONJ ejpam-6732 280 2 ∥f∥mbmo ∥f∥mbmo NUM ejpam-6732 280 3 sup sup NOUN ejpam-6732 280 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 280 5 2−m0γu 2−m0γu NUM ejpam-6732 281 1 ∞∑ ∞∑ PRON ejpam-6732 281 2 i=0 i=0 PROPN ejpam-6732 281 3 i∑ i∑ PROPN ejpam-6732 281 4 j=−∞ j=−∞ NOUN ejpam-6732 281 5 |λj |λj PRON ejpam-6732 281 6 |u |u ADJ ejpam-6732 281 7 2(−ui(n 2(−ui(n NUM ejpam-6732 281 8 / / SYM ejpam-6732 281 9 q1∞+v+n q1∞+v+n NOUN ejpam-6732 281 10 s s PART ejpam-6732 281 11 + + NOUN ejpam-6732 281 12 α∞))/2 α∞))/2 ADJ ejpam-6732 281 13 ≲ ≲ PROPN ejpam-6732 281 14 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 281 15 sup sup NOUN ejpam-6732 281 16 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 282 1 2−m0γu 2−m0γu NUM ejpam-6732 282 2 m0∑ m0∑ PROPN ejpam-6732 282 3 i=−∞ i=−∞ PRON ejpam-6732 282 4 |λi|u |λi|u NOUN ejpam-6732 282 5 + + CCONJ ejpam-6732 282 6 ∥f∥mbmo ∥f∥mbmo PUNCT ejpam-6732 282 7 λ λ SYM ejpam-6732 282 8 sup sup NOUN ejpam-6732 282 9 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 282 10 2−m0γu 2−m0γu NUM ejpam-6732 282 11 ∞∑ ∞∑ DET ejpam-6732 282 12 i=0 i=0 PROPN ejpam-6732 282 13 2(−ui(n 2(−ui(n NUM ejpam-6732 282 14 / / SYM ejpam-6732 282 15 q1∞+v+n q1∞+v+n NOUN ejpam-6732 282 16 s s PART ejpam-6732 282 17 + + NOUN ejpam-6732 282 18 α∞))/2 α∞))/2 ADJ ejpam-6732 282 19 ≲ ≲ PROPN ejpam-6732 282 20 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 282 21 λ λ PROPN ejpam-6732 282 22 . . PROPN ejpam-6732 282 23 second second ADJ ejpam-6732 282 24 , , PUNCT ejpam-6732 282 25 we we PRON ejpam-6732 282 26 estimate estimate VERB ejpam-6732 282 27 i2 i2 PROPN ejpam-6732 282 28 . . PUNCT ejpam-6732 283 1 therefore therefore ADV ejpam-6732 283 2 , , PUNCT ejpam-6732 283 3 when when SCONJ ejpam-6732 283 4 0 0 NUM ejpam-6732 283 5 < < X ejpam-6732 283 6 u u X ejpam-6732 283 7 ≤ ≤ NOUN ejpam-6732 283 8 1 1 NUM ejpam-6732 283 9 , , PUNCT ejpam-6732 283 10 we we PRON ejpam-6732 283 11 get get VERB ejpam-6732 283 12 i2 i2 NOUN ejpam-6732 283 13 = = PUNCT ejpam-6732 283 14 sup sup NOUN ejpam-6732 283 15 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 284 1 2−m0γu 2−m0γu NUM ejpam-6732 284 2 m0∑ m0∑ PROPN ejpam-6732 284 3 k=−∞ k=−∞ PROPN ejpam-6732 284 4 2kα(0)u 2kα(0)u NUM ejpam-6732 285 1 ( ( PUNCT ejpam-6732 285 2 k−1∑ k−1∑ PROPN ejpam-6732 285 3 i=−∞ i=−∞ NUM ejpam-6732 285 4 |λi| |λi| NOUN ejpam-6732 285 5 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 285 6 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 285 7 ) ) PUNCT ejpam-6732 286 1 [ [ X ejpam-6732 286 2 b b X ejpam-6732 286 3 , , PUNCT ejpam-6732 286 4 µφ µφ PROPN ejpam-6732 286 5 ] ] X ejpam-6732 286 6 m m VERB ejpam-6732 286 7 β β X ejpam-6732 286 8 bi bi NOUN ejpam-6732 286 9 ) ) PUNCT ejpam-6732 286 10 χk χk PROPN ejpam-6732 286 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 286 12 q2 q2 NOUN ejpam-6732 286 13 ( ( PUNCT ejpam-6732 286 14 · · PUNCT ejpam-6732 286 15 ) ) PUNCT ejpam-6732 286 16 ) ) PUNCT ejpam-6732 286 17 u u PROPN ejpam-6732 286 18 b. b. PROPN ejpam-6732 286 19 sultan sultan PROPN ejpam-6732 286 20 et et PROPN ejpam-6732 286 21 al al PROPN ejpam-6732 286 22 . . PUNCT ejpam-6732 286 23 / / SYM ejpam-6732 286 24 eur eur PROPN ejpam-6732 286 25 . . PUNCT ejpam-6732 287 1 j. j. PROPN ejpam-6732 287 2 pure pure PROPN ejpam-6732 287 3 appl appl PROPN ejpam-6732 287 4 . . PROPN ejpam-6732 287 5 math math PROPN ejpam-6732 287 6 , , PUNCT ejpam-6732 287 7 18 18 NUM ejpam-6732 287 8 ( ( PUNCT ejpam-6732 287 9 4 4 NUM ejpam-6732 287 10 ) ) PUNCT ejpam-6732 287 11 ( ( PUNCT ejpam-6732 287 12 2025 2025 NUM ejpam-6732 287 13 ) ) PUNCT ejpam-6732 287 14 , , PUNCT ejpam-6732 287 15 6732 6732 NUM ejpam-6732 287 16 13 13 NUM ejpam-6732 287 17 of of ADP ejpam-6732 287 18 20 20 NUM ejpam-6732 287 19 ≲ ≲ PROPN ejpam-6732 287 20 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 287 21 sup sup NOUN ejpam-6732 287 22 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 288 1 2−m0γu 2−m0γu NUM ejpam-6732 288 2 m0∑ m0∑ PROPN ejpam-6732 288 3 k=−∞ k=−∞ PROPN ejpam-6732 288 4 2α(0)ku 2α(0)ku NUM ejpam-6732 288 5 ( ( PUNCT ejpam-6732 288 6 k−1∑ k−1∑ PROPN ejpam-6732 288 7 i=−∞ i=−∞ NUM ejpam-6732 288 8 |λi| |λi| NOUN ejpam-6732 288 9 2−kn2−iv2k(v+ 2−kn2−iv2k(v+ NUM ejpam-6732 288 10 n n NOUN ejpam-6732 288 11 s s PART ejpam-6732 288 12 ) ) PUNCT ejpam-6732 288 13 ∥χbk ∥χbk NUM ejpam-6732 288 14 ∥q1 ∥q1 NOUN ejpam-6732 288 15 ( ( PUNCT ejpam-6732 288 16 · · PUNCT ejpam-6732 288 17 ) ) PUNCT ejpam-6732 288 18 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 288 19 ( ( PUNCT ejpam-6732 288 20 · · PUNCT ejpam-6732 288 21 ) ) PUNCT ejpam-6732 288 22 ( ( PUNCT ejpam-6732 288 23 k k NOUN ejpam-6732 288 24 − − PROPN ejpam-6732 288 25 i)m2−αii i)m2−αii NOUN ejpam-6732 288 26 ) ) PUNCT ejpam-6732 288 27 u u PROPN ejpam-6732 288 28 ≲ ≲ PROPN ejpam-6732 288 29 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 288 30 sup sup NOUN ejpam-6732 288 31 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 288 32 2−m0γu 2−m0γu NUM ejpam-6732 288 33 m0∑ m0∑ PROPN ejpam-6732 288 34 k=−∞ k=−∞ PROPN ejpam-6732 288 35 2kα(0)u 2kα(0)u NUM ejpam-6732 288 36 ( ( PUNCT ejpam-6732 288 37 k−1∑ k−1∑ PROPN ejpam-6732 288 38 i=−∞ i=−∞ PRON ejpam-6732 288 39 |λi|u |λi|u VERB ejpam-6732 288 40 2−α(0)iu2u(i−k)(n 2−α(0)iu2u(i−k)(n NUM ejpam-6732 288 41 / / SYM ejpam-6732 288 42 q′1(0)−v−n q′1(0)−v−n PROPN ejpam-6732 288 43 s s PART ejpam-6732 288 44 ) ) PUNCT ejpam-6732 288 45 ( ( PUNCT ejpam-6732 288 46 k k PROPN ejpam-6732 288 47 − − PROPN ejpam-6732 288 48 i)mu i)mu PROPN ejpam-6732 288 49 ) ) PUNCT ejpam-6732 288 50 ≲ ≲ PROPN ejpam-6732 288 51 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 288 52 sup sup NOUN ejpam-6732 288 53 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 288 54 2−m0γu 2−m0γu NUM ejpam-6732 288 55 m0∑ m0∑ PROPN ejpam-6732 288 56 k=−∞ k=−∞ PROPN ejpam-6732 289 1 k−1∑ k−1∑ AUX ejpam-6732 289 2 i=−∞ i=−∞ X ejpam-6732 289 3 |λi|u |λi|u NOUN ejpam-6732 289 4 2v1(i−k)u(k 2v1(i−k)u(k ADJ ejpam-6732 289 5 − − PUNCT ejpam-6732 290 1 i)mu i)mu PROPN ejpam-6732 290 2 ≲ ≲ PROPN ejpam-6732 290 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 290 4 sup sup NOUN ejpam-6732 290 5 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 290 6 2−m0γu 2−m0γu NUM ejpam-6732 290 7 −1∑ −1∑ PROPN ejpam-6732 290 8 i=−∞ i=−∞ NOUN ejpam-6732 290 9 |λi|u |λi|u NOUN ejpam-6732 290 10 i∑ i∑ PROPN ejpam-6732 290 11 k=−∞ k=−∞ NOUN ejpam-6732 290 12 2v1(i−k)u(k 2v1(i−k)u(k NUM ejpam-6732 290 13 − − PRON ejpam-6732 291 1 i)mu i)mu PROPN ejpam-6732 291 2 ≲ ≲ PROPN ejpam-6732 291 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 291 4 sup sup NOUN ejpam-6732 291 5 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 292 1 2−m0γu 2−m0γu NUM ejpam-6732 292 2 m0∑ m0∑ PROPN ejpam-6732 292 3 i=−∞ i=−∞ PRON ejpam-6732 292 4 |λi|u |λi|u ADP ejpam-6732 292 5 ≲ ≲ PROPN ejpam-6732 292 6 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 292 7 λ λ PROPN ejpam-6732 292 8 . . PUNCT ejpam-6732 293 1 now now ADV ejpam-6732 293 2 we we PRON ejpam-6732 293 3 will will AUX ejpam-6732 293 4 the the DET ejpam-6732 293 5 estimate estimate VERB ejpam-6732 293 6 for for ADP ejpam-6732 293 7 the the DET ejpam-6732 293 8 second second ADJ ejpam-6732 293 9 case case NOUN ejpam-6732 293 10 when when SCONJ ejpam-6732 293 11 1 1 NUM ejpam-6732 293 12 < < X ejpam-6732 293 13 u u X ejpam-6732 293 14 < < X ejpam-6732 293 15 ∞. ∞. PROPN ejpam-6732 293 16 let let VERB ejpam-6732 293 17 1 1 NUM ejpam-6732 293 18 u u NOUN ejpam-6732 293 19 + + NOUN ejpam-6732 293 20 1 1 NUM ejpam-6732 293 21 u′ u′ NOUN ejpam-6732 293 22 = = SYM ejpam-6732 293 23 1 1 NUM ejpam-6732 293 24 , , PUNCT ejpam-6732 293 25 we we PRON ejpam-6732 293 26 obtain obtain VERB ejpam-6732 293 27 i2 i2 NOUN ejpam-6732 293 28 = = PUNCT ejpam-6732 294 1 sup sup NOUN ejpam-6732 294 2 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 295 1 2−m0γu 2−m0γu NUM ejpam-6732 295 2 m0∑ m0∑ PROPN ejpam-6732 295 3 k=−∞ k=−∞ PROPN ejpam-6732 295 4 2kα(0)u 2kα(0)u NUM ejpam-6732 296 1 ( ( PUNCT ejpam-6732 296 2 k−1∑ k−1∑ PROPN ejpam-6732 296 3 i=−∞ i=−∞ NUM ejpam-6732 296 4 |λi| |λi| NOUN ejpam-6732 296 5 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 296 6 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 296 7 ) ) PUNCT ejpam-6732 297 1 [ [ X ejpam-6732 297 2 b b X ejpam-6732 297 3 , , PUNCT ejpam-6732 297 4 µφ µφ PROPN ejpam-6732 297 5 ] ] X ejpam-6732 297 6 m m VERB ejpam-6732 297 7 β β X ejpam-6732 297 8 bi bi NOUN ejpam-6732 297 9 ) ) PUNCT ejpam-6732 297 10 χk χk PROPN ejpam-6732 297 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 297 12 q2 q2 NOUN ejpam-6732 297 13 ( ( PUNCT ejpam-6732 297 14 · · PUNCT ejpam-6732 297 15 ) ) PUNCT ejpam-6732 297 16 ) ) PUNCT ejpam-6732 298 1 u u PROPN ejpam-6732 298 2 ≲ ≲ PROPN ejpam-6732 298 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 298 4 sup sup NOUN ejpam-6732 298 5 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 299 1 2−m0γu 2−m0γu NUM ejpam-6732 299 2 m0∑ m0∑ PROPN ejpam-6732 299 3 k=−∞ k=−∞ PROPN ejpam-6732 299 4 2α(0)ku 2α(0)ku NUM ejpam-6732 299 5 ( ( PUNCT ejpam-6732 299 6 k−1∑ k−1∑ PROPN ejpam-6732 299 7 i=−∞ i=−∞ NUM ejpam-6732 299 8 |λi| |λi| NOUN ejpam-6732 299 9 2−kn2−iv2k(v+ 2−kn2−iv2k(v+ NUM ejpam-6732 299 10 n n NOUN ejpam-6732 299 11 s s PART ejpam-6732 299 12 ) ) PUNCT ejpam-6732 299 13 ∥χbk ∥χbk NUM ejpam-6732 299 14 ∥q1 ∥q1 NOUN ejpam-6732 299 15 ( ( PUNCT ejpam-6732 299 16 · · PUNCT ejpam-6732 299 17 ) ) PUNCT ejpam-6732 299 18 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 299 19 ( ( PUNCT ejpam-6732 299 20 · · PUNCT ejpam-6732 299 21 ) ) PUNCT ejpam-6732 299 22 ( ( PUNCT ejpam-6732 299 23 k k NOUN ejpam-6732 299 24 − − PROPN ejpam-6732 299 25 i)m2−αii i)m2−αii NOUN ejpam-6732 299 26 ) ) PUNCT ejpam-6732 299 27 u u PROPN ejpam-6732 299 28 ≲ ≲ PROPN ejpam-6732 299 29 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 299 30 sup sup NOUN ejpam-6732 299 31 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 299 32 2−m0γu 2−m0γu NUM ejpam-6732 299 33 m0∑ m0∑ PROPN ejpam-6732 299 34 k=−∞ k=−∞ PROPN ejpam-6732 299 35 2kα(0)u 2kα(0)u NUM ejpam-6732 299 36 ( ( PUNCT ejpam-6732 299 37 −1∑ −1∑ PROPN ejpam-6732 299 38 i i PROPN ejpam-6732 299 39 = = PROPN ejpam-6732 299 40 k k X ejpam-6732 299 41 |λi|u |λi|u NOUN ejpam-6732 299 42 2−α(0)iu2u(i−k)(n 2−α(0)iu2u(i−k)(n NUM ejpam-6732 299 43 / / SYM ejpam-6732 299 44 q′1(0)−v−n q′1(0)−v−n PROPN ejpam-6732 299 45 s s PART ejpam-6732 299 46 ) ) PUNCT ejpam-6732 299 47 ( ( PUNCT ejpam-6732 299 48 k k PROPN ejpam-6732 299 49 − − PROPN ejpam-6732 299 50 i)mu i)mu PROPN ejpam-6732 299 51 ) ) PUNCT ejpam-6732 300 1 ≲ ≲ PROPN ejpam-6732 300 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 300 3 sup sup NOUN ejpam-6732 300 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 301 1 2−m0γu 2−m0γu NUM ejpam-6732 301 2 m0∑ m0∑ PROPN ejpam-6732 301 3 k=−∞ k=−∞ PROPN ejpam-6732 302 1 ( ( PUNCT ejpam-6732 302 2 −1∑ −1∑ PROPN ejpam-6732 302 3 i i PROPN ejpam-6732 302 4 = = PROPN ejpam-6732 302 5 k k X ejpam-6732 302 6 |λi|u |λi|u NOUN ejpam-6732 302 7 2v1(i−k)u/2 2v1(i−k)u/2 NUM ejpam-6732 302 8 ) ) PUNCT ejpam-6732 302 9 × × NOUN ejpam-6732 302 10 ( ( PUNCT ejpam-6732 302 11 −1∑ −1∑ PROPN ejpam-6732 302 12 i i PROPN ejpam-6732 302 13 = = PROPN ejpam-6732 302 14 k k PROPN ejpam-6732 302 15 2α(0)(k−i)u′/2(k 2α(0)(k−i)u′/2(k NOUN ejpam-6732 302 16 − − PROPN ejpam-6732 302 17 i)mu′/2 i)mu′/2 NOUN ejpam-6732 302 18 ) ) PUNCT ejpam-6732 302 19 u u NOUN ejpam-6732 302 20 / / SYM ejpam-6732 302 21 u′ u′ PROPN ejpam-6732 302 22 ≲ ≲ PROPN ejpam-6732 302 23 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 302 24 sup sup NOUN ejpam-6732 302 25 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 303 1 2−m0γu 2−m0γu NUM ejpam-6732 303 2 m0∑ m0∑ PROPN ejpam-6732 303 3 k=−∞ k=−∞ PROPN ejpam-6732 304 1 ( ( PUNCT ejpam-6732 304 2 −1∑ −1∑ PROPN ejpam-6732 304 3 i i PROPN ejpam-6732 304 4 = = PROPN ejpam-6732 304 5 k k X ejpam-6732 304 6 |λi|u |λi|u NOUN ejpam-6732 304 7 2v1(i−k)u/2 2v1(i−k)u/2 NUM ejpam-6732 304 8 ) ) PUNCT ejpam-6732 305 1 ≲ ≲ PROPN ejpam-6732 305 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 305 3 sup sup NOUN ejpam-6732 305 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 305 5 2−m0γu 2−m0γu NUM ejpam-6732 305 6 −1∑ −1∑ PROPN ejpam-6732 305 7 i=−∞ i=−∞ NOUN ejpam-6732 305 8 |λi|u |λi|u NOUN ejpam-6732 305 9 i∑ i∑ PROPN ejpam-6732 305 10 k=−∞ k=−∞ NOUN ejpam-6732 305 11 2v1(i−k)u/2 2v1(i−k)u/2 NUM ejpam-6732 306 1 ≲ ≲ PROPN ejpam-6732 306 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 306 3 sup sup NOUN ejpam-6732 306 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 306 5 2−m0γu 2−m0γu NUM ejpam-6732 306 6 −1∑ −1∑ PROPN ejpam-6732 306 7 i=−∞ i=−∞ NOUN ejpam-6732 306 8 |λi|u |λi|u NOUN ejpam-6732 306 9 i∑ i∑ PROPN ejpam-6732 306 10 k=−∞ k=−∞ NOUN ejpam-6732 306 11 2v1(i−k)u/2 2v1(i−k)u/2 NUM ejpam-6732 307 1 ≲ ≲ PROPN ejpam-6732 307 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 307 3 sup sup NOUN ejpam-6732 307 4 m0<0,m0∈z m0<0,m0∈z NOUN ejpam-6732 308 1 2−m0γu 2−m0γu NUM ejpam-6732 308 2 m0∑ m0∑ PROPN ejpam-6732 308 3 i=−∞ i=−∞ PRON ejpam-6732 308 4 |λi|u |λi|u PROPN ejpam-6732 308 5 b. b. PROPN ejpam-6732 308 6 sultan sultan PROPN ejpam-6732 308 7 et et PROPN ejpam-6732 308 8 al al PROPN ejpam-6732 308 9 . . PUNCT ejpam-6732 308 10 / / SYM ejpam-6732 308 11 eur eur PROPN ejpam-6732 308 12 . . PUNCT ejpam-6732 309 1 j. j. PROPN ejpam-6732 309 2 pure pure PROPN ejpam-6732 309 3 appl appl PROPN ejpam-6732 309 4 . . PROPN ejpam-6732 309 5 math math PROPN ejpam-6732 309 6 , , PUNCT ejpam-6732 309 7 18 18 NUM ejpam-6732 309 8 ( ( PUNCT ejpam-6732 309 9 4 4 NUM ejpam-6732 309 10 ) ) PUNCT ejpam-6732 309 11 ( ( PUNCT ejpam-6732 309 12 2025 2025 NUM ejpam-6732 309 13 ) ) PUNCT ejpam-6732 309 14 , , PUNCT ejpam-6732 309 15 6732 6732 NUM ejpam-6732 309 16 14 14 NUM ejpam-6732 309 17 of of ADP ejpam-6732 309 18 20 20 NUM ejpam-6732 309 19 ≲ ≲ PROPN ejpam-6732 309 20 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 309 21 λ λ PROPN ejpam-6732 309 22 . . PUNCT ejpam-6732 310 1 finally finally ADV ejpam-6732 310 2 , , PUNCT ejpam-6732 310 3 we we PRON ejpam-6732 310 4 estimate estimate VERB ejpam-6732 310 5 iii iii NUM ejpam-6732 310 6 : : PUNCT ejpam-6732 310 7 iii iii X ejpam-6732 310 8 = = SYM ejpam-6732 310 9 sup sup NOUN ejpam-6732 310 10 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 310 11 2−m0γu 2−m0γu NUM ejpam-6732 310 12 m0∑ m0∑ PROPN ejpam-6732 310 13 k=0 k=0 PROPN ejpam-6732 310 14 2kα∞u 2kα∞u NUM ejpam-6732 310 15 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 310 16 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 310 17 ) ) PUNCT ejpam-6732 311 1 [ [ X ejpam-6732 311 2 b b X ejpam-6732 311 3 , , PUNCT ejpam-6732 311 4 µφ µφ PROPN ejpam-6732 311 5 ] ] X ejpam-6732 311 6 m m VERB ejpam-6732 311 7 β β X ejpam-6732 311 8 f f PROPN ejpam-6732 311 9 ) ) PUNCT ejpam-6732 311 10 χk χk PROPN ejpam-6732 311 11 ∥∥∥u ∥∥∥u PROPN ejpam-6732 311 12 q2 q2 PROPN ejpam-6732 311 13 ( ( PUNCT ejpam-6732 311 14 · · PUNCT ejpam-6732 311 15 ) ) PUNCT ejpam-6732 311 16 ≲ ≲ PROPN ejpam-6732 311 17 sup sup NOUN ejpam-6732 311 18 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 311 19 2−m0γu 2−m0γu NUM ejpam-6732 311 20 m0∑ m0∑ PROPN ejpam-6732 311 21 k=0 k=0 PROPN ejpam-6732 311 22 2kα∞u 2kα∞u NUM ejpam-6732 311 23 ( ( PUNCT ejpam-6732 311 24 ∞∑ ∞∑ NUM ejpam-6732 311 25 i i PROPN ejpam-6732 311 26 = = PROPN ejpam-6732 311 27 k k X ejpam-6732 311 28 |λi| |λi| NOUN ejpam-6732 311 29 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 311 30 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 311 31 ) ) PUNCT ejpam-6732 312 1 [ [ X ejpam-6732 312 2 b b X ejpam-6732 312 3 , , PUNCT ejpam-6732 312 4 µφ µφ PROPN ejpam-6732 312 5 ] ] X ejpam-6732 312 6 m m VERB ejpam-6732 312 7 β β X ejpam-6732 312 8 bi bi NOUN ejpam-6732 312 9 ) ) PUNCT ejpam-6732 312 10 χk χk PROPN ejpam-6732 312 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 312 12 q2 q2 NOUN ejpam-6732 312 13 ( ( PUNCT ejpam-6732 312 14 · · PUNCT ejpam-6732 312 15 ) ) PUNCT ejpam-6732 312 16 ) ) PUNCT ejpam-6732 312 17 u u NOUN ejpam-6732 312 18 + + NOUN ejpam-6732 312 19 sup sup PROPN ejpam-6732 312 20 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 312 21 2−m0γu 2−m0γu NUM ejpam-6732 312 22 m0∑ m0∑ PROPN ejpam-6732 312 23 k=0 k=0 PROPN ejpam-6732 312 24 2kα∞u 2kα∞u NUM ejpam-6732 312 25 ( ( PUNCT ejpam-6732 312 26 k−1∑ k−1∑ PROPN ejpam-6732 312 27 i=−∞ i=−∞ NUM ejpam-6732 312 28 |λi| |λi| NOUN ejpam-6732 312 29 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 312 30 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 312 31 ) ) PUNCT ejpam-6732 313 1 [ [ X ejpam-6732 313 2 b b X ejpam-6732 313 3 , , PUNCT ejpam-6732 313 4 µφ µφ PROPN ejpam-6732 313 5 ] ] X ejpam-6732 313 6 m m VERB ejpam-6732 313 7 β β X ejpam-6732 313 8 bi bi NOUN ejpam-6732 313 9 ) ) PUNCT ejpam-6732 313 10 χk χk PROPN ejpam-6732 313 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 313 12 q2 q2 NOUN ejpam-6732 313 13 ( ( PUNCT ejpam-6732 313 14 · · PUNCT ejpam-6732 313 15 ) ) PUNCT ejpam-6732 313 16 ) ) PUNCT ejpam-6732 313 17 u u NOUN ejpam-6732 313 18 : : PUNCT ejpam-6732 313 19 = = PUNCT ejpam-6732 313 20 iii1 iii1 PROPN ejpam-6732 313 21 + + NUM ejpam-6732 313 22 iii2 iii2 NOUN ejpam-6732 313 23 . . PUNCT ejpam-6732 314 1 if if SCONJ ejpam-6732 314 2 k k PROPN ejpam-6732 314 3 ∈ ∈ PROPN ejpam-6732 314 4 z z PROPN ejpam-6732 314 5 and and CCONJ ejpam-6732 314 6 i i PRON ejpam-6732 314 7 ≥ ≥ AUX ejpam-6732 314 8 k k NOUN ejpam-6732 315 1 + + CCONJ ejpam-6732 315 2 1 1 NUM ejpam-6732 315 3 and and CCONJ ejpam-6732 315 4 a.e a.e PROPN ejpam-6732 315 5 . . PROPN ejpam-6732 315 6 z1 z1 PROPN ejpam-6732 315 7 ∈ ∈ PROPN ejpam-6732 315 8 fk fk INTJ ejpam-6732 315 9 , , PUNCT ejpam-6732 315 10 z2 z2 PROPN ejpam-6732 315 11 ∈ ∈ PROPN ejpam-6732 315 12 fi fi NOUN ejpam-6732 315 13 , , PUNCT ejpam-6732 315 14 then then ADV ejpam-6732 315 15 |z1 |z1 PROPN ejpam-6732 315 16 − − PROPN ejpam-6732 315 17 z2| z2| PROPN ejpam-6732 316 1 ≈ ≈ PROPN ejpam-6732 316 2 |z2| |z2| PROPN ejpam-6732 317 1 ≈ ≈ PROPN ejpam-6732 317 2 2i 2i NUM ejpam-6732 317 3 , , PUNCT ejpam-6732 317 4 |µφ(bi)(z1)| |µφ(bi)(z1)| NOUN ejpam-6732 317 5 ≤ ≤ X ejpam-6732 317 6   X ejpam-6732 317 7 |z2|∫ |z2|∫ PROPN ejpam-6732 317 8 o o X ejpam-6732 317 9 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ PROPN ejpam-6732 317 10 ∫ ∫ PROPN ejpam-6732 317 11 |z1−z2|≤t |z1−z2|≤t PROPN ejpam-6732 317 12 φ(z1 φ(z1 NOUN ejpam-6732 317 13 − − PROPN ejpam-6732 317 14 z2 z2 PROPN ejpam-6732 317 15 ) ) PUNCT ejpam-6732 317 16 |z1 |z1 PROPN ejpam-6732 317 17 − − PROPN ejpam-6732 317 18 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 317 19 ) ) PUNCT ejpam-6732 317 20 bi(z2)dz2 bi(z2)dz2 NOUN ejpam-6732 317 21 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ NOUN ejpam-6732 317 22 2 2 NUM ejpam-6732 317 23 dt dt NOUN ejpam-6732 317 24 t3 t3 PROPN ejpam-6732 317 25   PROPN ejpam-6732 317 26 1/2 1/2 NUM ejpam-6732 317 27 + + NUM ejpam-6732 317 28   NOUN ejpam-6732 317 29 ∞∫ ∞∫ PROPN ejpam-6732 317 30 |z2| |z2| PROPN ejpam-6732 317 31 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ PROPN ejpam-6732 317 32 ∫ ∫ PROPN ejpam-6732 317 33 |z1−z2|≤t |z1−z2|≤t PROPN ejpam-6732 317 34 φ(z1 φ(z1 PROPN ejpam-6732 317 35 − − PROPN ejpam-6732 317 36 z2 z2 PROPN ejpam-6732 317 37 ) ) PUNCT ejpam-6732 317 38 |z1 |z1 PROPN ejpam-6732 317 39 − − PROPN ejpam-6732 317 40 z2|n−1−β(z1 z2|n−1−β(z1 PROPN ejpam-6732 317 41 ) ) PUNCT ejpam-6732 317 42 bi(z2)dz2 bi(z2)dz2 NOUN ejpam-6732 317 43 ∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣ NOUN ejpam-6732 317 44 2 2 NUM ejpam-6732 317 45 dt dt NOUN ejpam-6732 317 46 t3 t3 PROPN ejpam-6732 317 47   PROPN ejpam-6732 317 48 1/2 1/2 NUM ejpam-6732 317 49 = = NOUN ejpam-6732 317 50 : : PUNCT ejpam-6732 317 51 i31 i31 NOUN ejpam-6732 317 52 + + CCONJ ejpam-6732 317 53 i32 i32 NOUN ejpam-6732 317 54 . . PUNCT ejpam-6732 318 1 it it PRON ejpam-6732 318 2 is be AUX ejpam-6732 318 3 easy easy ADJ ejpam-6732 318 4 to to PART ejpam-6732 318 5 find find VERB ejpam-6732 318 6 that that SCONJ ejpam-6732 318 7 i31 i31 NOUN ejpam-6732 318 8 ≤2(i−k)/22−in ≤2(i−k)/22−in PROPN ejpam-6732 318 9 |z1|β(z1 |z1|β(z1 PROPN ejpam-6732 318 10 ) ) PUNCT ejpam-6732 318 11 ∥bi(z2)∥q1 ∥bi(z2)∥q1 NOUN ejpam-6732 318 12 ( ( PUNCT ejpam-6732 318 13 · · PUNCT ejpam-6732 318 14 ) ) PUNCT ejpam-6732 318 15 ( ( PUNCT ejpam-6732 318 16 |b(z1)− |b(z1)− NOUN ejpam-6732 318 17 bbi bbi VERB ejpam-6732 318 18 | | ADV ejpam-6732 318 19 m m VERB ejpam-6732 318 20 ∥φ(z1 ∥φ(z1 ADJ ejpam-6732 318 21 − − NOUN ejpam-6732 318 22 · · PUNCT ejpam-6732 318 23 ) ) PUNCT ejpam-6732 318 24 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 318 25 ( ( PUNCT ejpam-6732 318 26 · · PUNCT ejpam-6732 318 27 ) ) PUNCT ejpam-6732 319 1 + + NUM ejpam-6732 319 2 ∥(b(·)− ∥(b(·)− NUM ejpam-6732 319 3 bbi bbi ADJ ejpam-6732 319 4 ) ) PUNCT ejpam-6732 319 5 m(φ(z1 m(φ(z1 NOUN ejpam-6732 319 6 − − PROPN ejpam-6732 319 7 · · PUNCT ejpam-6732 319 8 ) ) PUNCT ejpam-6732 319 9 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 319 10 ( ( PUNCT ejpam-6732 319 11 · · PUNCT ejpam-6732 319 12 ) ) PUNCT ejpam-6732 319 13 ) ) PUNCT ejpam-6732 319 14 . . PUNCT ejpam-6732 320 1 similarly similarly ADV ejpam-6732 320 2 we we PRON ejpam-6732 320 3 have have VERB ejpam-6732 320 4 i32 i32 PROPN ejpam-6732 320 5 ≤2−in ≤2−in PROPN ejpam-6732 320 6 |z1|β(z1 |z1|β(z1 PROPN ejpam-6732 320 7 ) ) PUNCT ejpam-6732 320 8 ∥bi(z2)∥q1 ∥bi(z2)∥q1 NOUN ejpam-6732 320 9 ( ( PUNCT ejpam-6732 320 10 · · PUNCT ejpam-6732 320 11 ) ) PUNCT ejpam-6732 320 12 { { PUNCT ejpam-6732 320 13 |b(z1)− |b(z1)− NOUN ejpam-6732 320 14 bbi bbi VERB ejpam-6732 320 15 | | ADV ejpam-6732 320 16 m m VERB ejpam-6732 320 17 ∥φ(z1 ∥φ(z1 ADJ ejpam-6732 320 18 − − NOUN ejpam-6732 320 19 · · PUNCT ejpam-6732 320 20 ) ) PUNCT ejpam-6732 320 21 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 320 22 ( ( PUNCT ejpam-6732 320 23 · · PUNCT ejpam-6732 320 24 ) ) PUNCT ejpam-6732 321 1 + + NUM ejpam-6732 321 2 ∥(b(·)− ∥(b(·)− NUM ejpam-6732 321 3 bbi bbi ADJ ejpam-6732 321 4 ) ) PUNCT ejpam-6732 321 5 m(φ(z1 m(φ(z1 NOUN ejpam-6732 321 6 − − PROPN ejpam-6732 321 7 · · PUNCT ejpam-6732 321 8 ) ) PUNCT ejpam-6732 321 9 χi(·)∥q′1 χi(·)∥q′1 NOUN ejpam-6732 321 10 ( ( PUNCT ejpam-6732 321 11 · · PUNCT ejpam-6732 321 12 ) ) PUNCT ejpam-6732 321 13 } } PUNCT ejpam-6732 321 14 . . PUNCT ejpam-6732 322 1 ∥∥∥χk(1 ∥∥∥χk(1 PROPN ejpam-6732 322 2 + + SYM ejpam-6732 322 3 |z1|)−λ(z1 |z1|)−λ(z1 NOUN ejpam-6732 322 4 ) ) PUNCT ejpam-6732 323 1 [ [ X ejpam-6732 323 2 b b X ejpam-6732 323 3 , , PUNCT ejpam-6732 323 4 µφ µφ PROPN ejpam-6732 323 5 ] ] X ejpam-6732 323 6 m m VERB ejpam-6732 323 7 β β X ejpam-6732 323 8 ( ( PUNCT ejpam-6732 323 9 gχi gχi PROPN ejpam-6732 323 10 ) ) PUNCT ejpam-6732 323 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 323 12 q2 q2 NOUN ejpam-6732 323 13 ( ( PUNCT ejpam-6732 323 14 · · PUNCT ejpam-6732 323 15 ) ) PUNCT ejpam-6732 323 16 ≤ ≤ NUM ejpam-6732 323 17 c2−in c2−in NOUN ejpam-6732 323 18 ∥bi∥q1 ∥bi∥q1 X ejpam-6732 323 19 ( ( PUNCT ejpam-6732 323 20 · · PUNCT ejpam-6732 323 21 ) ) PUNCT ejpam-6732 323 22 { { PUNCT ejpam-6732 323 23 ∥∥∥(b(z1)− ∥∥∥(b(z1)− NOUN ejpam-6732 323 24 bbi bbi PROPN ejpam-6732 323 25 ) ) PUNCT ejpam-6732 323 26 m m PROPN ejpam-6732 323 27 |z1|β(z1 |z1|β(z1 ADJ ejpam-6732 323 28 ) ) PUNCT ejpam-6732 323 29 χk(z1)(1 χk(z1)(1 NOUN ejpam-6732 323 30 + + CCONJ ejpam-6732 323 31 |z1|)−λ(z1 |z1|)−λ(z1 NOUN ejpam-6732 323 32 ) ) PUNCT ejpam-6732 323 33 ∥∥∥ ∥∥∥ PROPN ejpam-6732 323 34 q2 q2 NOUN ejpam-6732 323 35 ( ( PUNCT ejpam-6732 323 36 · · PUNCT ejpam-6732 323 37 ) ) PUNCT ejpam-6732 323 38 2−iv2k(v+ 2−iv2k(v+ NUM ejpam-6732 323 39 n n SYM ejpam-6732 323 40 s s NOUN ejpam-6732 323 41 ) ) PUNCT ejpam-6732 323 42 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 323 43 ) ) PUNCT ejpam-6732 323 44 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 323 45 ( ( PUNCT ejpam-6732 323 46 · · PUNCT ejpam-6732 323 47 ) ) PUNCT ejpam-6732 324 1 + + CCONJ ejpam-6732 324 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 324 3 2−iv2k(v+ 2−iv2k(v+ NUM ejpam-6732 324 4 n n SYM ejpam-6732 324 5 s s PART ejpam-6732 324 6 ) ) PUNCT ejpam-6732 324 7 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 324 8 ) ) PUNCT ejpam-6732 324 9 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 324 10 ( ( PUNCT ejpam-6732 324 11 · · PUNCT ejpam-6732 324 12 ) ) PUNCT ejpam-6732 324 13 ∥∥∥|z1|β(z1 ∥∥∥|z1|β(z1 NUM ejpam-6732 324 14 ) ) PUNCT ejpam-6732 324 15 χk(z1)(1 χk(z1)(1 NOUN ejpam-6732 324 16 + + CCONJ ejpam-6732 324 17 |z1|)−λ(z1 |z1|)−λ(z1 NOUN ejpam-6732 324 18 ) ) PUNCT ejpam-6732 324 19 ∥∥∥ ∥∥∥ PROPN ejpam-6732 324 20 q2 q2 NOUN ejpam-6732 324 21 ( ( PUNCT ejpam-6732 324 22 · · PUNCT ejpam-6732 324 23 ) ) PUNCT ejpam-6732 324 24 } } PUNCT ejpam-6732 324 25 b. b. PROPN ejpam-6732 324 26 sultan sultan PROPN ejpam-6732 324 27 et et PROPN ejpam-6732 324 28 al al PROPN ejpam-6732 324 29 . . PUNCT ejpam-6732 324 30 / / SYM ejpam-6732 324 31 eur eur PROPN ejpam-6732 324 32 . . PUNCT ejpam-6732 325 1 j. j. PROPN ejpam-6732 325 2 pure pure PROPN ejpam-6732 325 3 appl appl PROPN ejpam-6732 325 4 . . PROPN ejpam-6732 325 5 math math PROPN ejpam-6732 325 6 , , PUNCT ejpam-6732 325 7 18 18 NUM ejpam-6732 325 8 ( ( PUNCT ejpam-6732 325 9 4 4 NUM ejpam-6732 325 10 ) ) PUNCT ejpam-6732 325 11 ( ( PUNCT ejpam-6732 325 12 2025 2025 NUM ejpam-6732 325 13 ) ) PUNCT ejpam-6732 325 14 , , PUNCT ejpam-6732 325 15 6732 6732 NUM ejpam-6732 325 16 15 15 NUM ejpam-6732 325 17 of of ADP ejpam-6732 325 18 20 20 NUM ejpam-6732 325 19 ≤ ≤ NUM ejpam-6732 325 20 c2−in c2−in NOUN ejpam-6732 325 21 ∥bi∥q1 ∥bi∥q1 X ejpam-6732 325 22 ( ( PUNCT ejpam-6732 325 23 · · PUNCT ejpam-6732 325 24 ) ) PUNCT ejpam-6732 325 25 { { PUNCT ejpam-6732 325 26 ( ( PUNCT ejpam-6732 325 27 k k NOUN ejpam-6732 325 28 − − PROPN ejpam-6732 325 29 i)m i)m NOUN ejpam-6732 325 30 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 325 31 ∥χbk ∥χbk NUM ejpam-6732 325 32 ∥q1 ∥q1 NOUN ejpam-6732 325 33 ( ( PUNCT ejpam-6732 325 34 · · PUNCT ejpam-6732 325 35 ) ) PUNCT ejpam-6732 325 36 2 2 NUM ejpam-6732 325 37 −iv2k(v+ −iv2k(v+ PROPN ejpam-6732 325 38 n n PART ejpam-6732 325 39 s s PART ejpam-6732 325 40 ) ) PUNCT ejpam-6732 325 41 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 325 42 ) ) PUNCT ejpam-6732 325 43 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 325 44 ( ( PUNCT ejpam-6732 325 45 · · PUNCT ejpam-6732 325 46 ) ) PUNCT ejpam-6732 326 1 + + CCONJ ejpam-6732 326 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 326 3 2−iv2k(v+ 2−iv2k(v+ NUM ejpam-6732 326 4 n n SYM ejpam-6732 326 5 s s PART ejpam-6732 326 6 ) ) PUNCT ejpam-6732 326 7 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 326 8 ) ) PUNCT ejpam-6732 326 9 ∥ ∥ PUNCT ejpam-6732 326 10 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 326 11 ( ( PUNCT ejpam-6732 326 12 · · PUNCT ejpam-6732 326 13 ) ) PUNCT ejpam-6732 326 14 ∥χbk ∥χbk NUM ejpam-6732 326 15 ∥q1 ∥q1 NOUN ejpam-6732 326 16 ( ( PUNCT ejpam-6732 326 17 · · PUNCT ejpam-6732 326 18 ) ) PUNCT ejpam-6732 326 19 } } PUNCT ejpam-6732 326 20 ≤ ≤ NUM ejpam-6732 326 21 c2−in c2−in NOUN ejpam-6732 326 22 ∥bi∥q1 ∥bi∥q1 X ejpam-6732 326 23 ( ( PUNCT ejpam-6732 326 24 · · PUNCT ejpam-6732 326 25 ) ) PUNCT ejpam-6732 326 26 ( ( PUNCT ejpam-6732 326 27 k k NOUN ejpam-6732 326 28 − − PROPN ejpam-6732 326 29 i)m i)m NOUN ejpam-6732 326 30 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 326 31 ∥χbk ∥χbk NUM ejpam-6732 326 32 ∥q1 ∥q1 NOUN ejpam-6732 326 33 ( ( PUNCT ejpam-6732 326 34 · · PUNCT ejpam-6732 326 35 ) ) PUNCT ejpam-6732 326 36 2 2 NUM ejpam-6732 326 37 −iv2k(v+ −iv2k(v+ PROPN ejpam-6732 326 38 n n PART ejpam-6732 326 39 s s PART ejpam-6732 326 40 ) ) PUNCT ejpam-6732 326 41 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 X ejpam-6732 326 42 ) ) PUNCT ejpam-6732 326 43 ∥χbi∥q1 ∥χbi∥q1 NOUN ejpam-6732 326 44 ( ( PUNCT ejpam-6732 326 45 · · PUNCT ejpam-6732 326 46 ) ) PUNCT ejpam-6732 326 47 ≤ ≤ NUM ejpam-6732 326 48 c(k c(k PROPN ejpam-6732 326 49 − − NOUN ejpam-6732 326 50 i)m i)m NOUN ejpam-6732 326 51 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 ADJ ejpam-6732 326 52 ) ) PUNCT ejpam-6732 326 53 ∥f∥ ∥f∥ PROPN ejpam-6732 326 54 m m PROPN ejpam-6732 326 55 bmo bmo NOUN ejpam-6732 326 56 2−in2−iv2k(v+ 2−in2−iv2k(v+ NUM ejpam-6732 326 57 n n PROPN ejpam-6732 326 58 s s PART ejpam-6732 326 59 ) ) PUNCT ejpam-6732 326 60 ∥χbk ∥χbk NUM ejpam-6732 326 61 ∥q1 ∥q1 NOUN ejpam-6732 326 62 ( ( PUNCT ejpam-6732 326 63 · · PUNCT ejpam-6732 326 64 ) ) PUNCT ejpam-6732 326 65 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 326 66 ( ( PUNCT ejpam-6732 326 67 · · PUNCT ejpam-6732 326 68 ) ) PUNCT ejpam-6732 326 69 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 326 70 ( ( PUNCT ejpam-6732 326 71 · · PUNCT ejpam-6732 326 72 ) ) PUNCT ejpam-6732 326 73 . . PUNCT ejpam-6732 327 1 therefore therefore ADV ejpam-6732 327 2 , , PUNCT ejpam-6732 327 3 when when SCONJ ejpam-6732 327 4 0 0 NUM ejpam-6732 327 5 < < X ejpam-6732 327 6 u u X ejpam-6732 327 7 ≤ ≤ ADV ejpam-6732 327 8 1 1 NUM ejpam-6732 327 9 and and CCONJ ejpam-6732 327 10 v2 v2 PROPN ejpam-6732 327 11 = = SYM ejpam-6732 327 12 v v NOUN ejpam-6732 327 13 + + CCONJ ejpam-6732 327 14 n n CCONJ ejpam-6732 327 15 s s NOUN ejpam-6732 327 16 + + CCONJ ejpam-6732 327 17 n n CCONJ ejpam-6732 327 18 q1∞ q1∞ PRON ejpam-6732 327 19 + + CCONJ ejpam-6732 327 20 α∞ α∞ NOUN ejpam-6732 327 21 , , PUNCT ejpam-6732 327 22 we we PRON ejpam-6732 327 23 get get VERB ejpam-6732 327 24 iii1 iii1 NOUN ejpam-6732 327 25 = = PUNCT ejpam-6732 327 26 sup sup NOUN ejpam-6732 327 27 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 327 28 2−m0γu 2−m0γu NUM ejpam-6732 327 29 m0∑ m0∑ PROPN ejpam-6732 327 30 k=0 k=0 PROPN ejpam-6732 327 31 2kα∞u 2kα∞u NUM ejpam-6732 327 32 ( ( PUNCT ejpam-6732 327 33 ∞∑ ∞∑ NUM ejpam-6732 327 34 i i PROPN ejpam-6732 327 35 = = PROPN ejpam-6732 327 36 k k X ejpam-6732 327 37 |λi| |λi| NOUN ejpam-6732 327 38 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 327 39 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 327 40 ) ) PUNCT ejpam-6732 328 1 [ [ X ejpam-6732 328 2 b b X ejpam-6732 328 3 , , PUNCT ejpam-6732 328 4 µφ µφ PROPN ejpam-6732 328 5 ] ] X ejpam-6732 328 6 m m VERB ejpam-6732 328 7 β β X ejpam-6732 328 8 bi bi NOUN ejpam-6732 328 9 ) ) PUNCT ejpam-6732 328 10 χk χk PROPN ejpam-6732 328 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 328 12 q2 q2 NOUN ejpam-6732 328 13 ( ( PUNCT ejpam-6732 328 14 · · PUNCT ejpam-6732 328 15 ) ) PUNCT ejpam-6732 328 16 ) ) PUNCT ejpam-6732 329 1 u u PROPN ejpam-6732 329 2 ≲ ≲ PROPN ejpam-6732 329 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 329 4 sup sup NOUN ejpam-6732 329 5 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 329 6 2−m0γu 2−m0γu NUM ejpam-6732 329 7 m0∑ m0∑ PROPN ejpam-6732 329 8 k=0 k=0 PROPN ejpam-6732 329 9 2kα∞u 2kα∞u NUM ejpam-6732 329 10 ( ( PUNCT ejpam-6732 329 11 ∞∑ ∞∑ NUM ejpam-6732 329 12 i i PROPN ejpam-6732 329 13 = = PROPN ejpam-6732 329 14 k k NOUN ejpam-6732 329 15 |λi| |λi| NOUN ejpam-6732 329 16 2−kn2−iv2k(v+ 2−kn2−iv2k(v+ NUM ejpam-6732 329 17 n n NOUN ejpam-6732 329 18 s s PART ejpam-6732 329 19 ) ) PUNCT ejpam-6732 329 20 ∥χbk ∥χbk NUM ejpam-6732 329 21 ∥q1 ∥q1 NOUN ejpam-6732 329 22 ( ( PUNCT ejpam-6732 329 23 · · PUNCT ejpam-6732 329 24 ) ) PUNCT ejpam-6732 329 25 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 329 26 ( ( PUNCT ejpam-6732 329 27 · · PUNCT ejpam-6732 329 28 ) ) PUNCT ejpam-6732 329 29 ( ( PUNCT ejpam-6732 329 30 k k NOUN ejpam-6732 329 31 − − PROPN ejpam-6732 329 32 i)m2−αii i)m2−αii NOUN ejpam-6732 329 33 ) ) PUNCT ejpam-6732 329 34 u u PROPN ejpam-6732 329 35 ≲ ≲ PROPN ejpam-6732 329 36 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 329 37 sup sup NOUN ejpam-6732 329 38 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 329 39 2−m0γu 2−m0γu NUM ejpam-6732 329 40 m0∑ m0∑ PROPN ejpam-6732 329 41 k=0 k=0 PROPN ejpam-6732 330 1 ∞∑ ∞∑ NUM ejpam-6732 330 2 i i PROPN ejpam-6732 330 3 = = PROPN ejpam-6732 330 4 k k X ejpam-6732 330 5 |λi|u |λi|u NOUN ejpam-6732 330 6 2v2(k−i)u(k 2v2(k−i)u(k NUM ejpam-6732 330 7 − − PROPN ejpam-6732 330 8 i)mu i)mu PROPN ejpam-6732 330 9 ≲ ≲ PROPN ejpam-6732 330 10 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 330 11 sup sup NOUN ejpam-6732 330 12 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 330 13 2−m0γu 2−m0γu NUM ejpam-6732 330 14 ∞∑ ∞∑ PRON ejpam-6732 330 15 i=0 i=0 ADJ ejpam-6732 330 16 |λi|u |λi|u NOUN ejpam-6732 330 17 i∑ i∑ PRON ejpam-6732 330 18 k=0 k=0 PROPN ejpam-6732 330 19 2v2(k−i)u(k 2v2(k−i)u(k NUM ejpam-6732 330 20 − − PROPN ejpam-6732 331 1 i)mu i)mu PROPN ejpam-6732 331 2 ≲ ≲ PROPN ejpam-6732 331 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 331 4 λ λ PROPN ejpam-6732 331 5 . . PUNCT ejpam-6732 332 1 now now ADV ejpam-6732 332 2 we we PRON ejpam-6732 332 3 will will AUX ejpam-6732 332 4 the the DET ejpam-6732 332 5 estimate estimate VERB ejpam-6732 332 6 for for ADP ejpam-6732 332 7 the the DET ejpam-6732 332 8 second second ADJ ejpam-6732 332 9 case case NOUN ejpam-6732 332 10 when when SCONJ ejpam-6732 332 11 1 1 NUM ejpam-6732 332 12 < < X ejpam-6732 332 13 u u X ejpam-6732 332 14 < < X ejpam-6732 332 15 ∞. ∞. PROPN ejpam-6732 332 16 let let VERB ejpam-6732 332 17 1 1 NUM ejpam-6732 332 18 u u NOUN ejpam-6732 332 19 + + NOUN ejpam-6732 332 20 1 1 NUM ejpam-6732 332 21 u′ u′ NOUN ejpam-6732 332 22 = = SYM ejpam-6732 332 23 1 1 NUM ejpam-6732 332 24 , , PUNCT ejpam-6732 332 25 we we PRON ejpam-6732 332 26 obtain obtain VERB ejpam-6732 332 27 iii1 iii1 NOUN ejpam-6732 333 1 = = PUNCT ejpam-6732 333 2 sup sup NOUN ejpam-6732 333 3 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 333 4 2−m0γu 2−m0γu NUM ejpam-6732 333 5 m0∑ m0∑ PROPN ejpam-6732 333 6 k=0 k=0 PROPN ejpam-6732 333 7 2kα∞u 2kα∞u NUM ejpam-6732 333 8 ( ( PUNCT ejpam-6732 333 9 ∞∑ ∞∑ NUM ejpam-6732 333 10 i i PROPN ejpam-6732 333 11 = = PROPN ejpam-6732 333 12 k k X ejpam-6732 333 13 |λi| |λi| NOUN ejpam-6732 333 14 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 333 15 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 333 16 ) ) PUNCT ejpam-6732 334 1 [ [ X ejpam-6732 334 2 b b X ejpam-6732 334 3 , , PUNCT ejpam-6732 334 4 µφ µφ PROPN ejpam-6732 334 5 ] ] X ejpam-6732 334 6 m m VERB ejpam-6732 334 7 β β X ejpam-6732 334 8 bi bi NOUN ejpam-6732 334 9 ) ) PUNCT ejpam-6732 334 10 χk χk PROPN ejpam-6732 334 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 334 12 q2 q2 NOUN ejpam-6732 334 13 ( ( PUNCT ejpam-6732 334 14 · · PUNCT ejpam-6732 334 15 ) ) PUNCT ejpam-6732 334 16 ) ) PUNCT ejpam-6732 335 1 u u PROPN ejpam-6732 335 2 ≲ ≲ PROPN ejpam-6732 335 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 335 4 sup sup NOUN ejpam-6732 335 5 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 335 6 2−m0γu 2−m0γu NUM ejpam-6732 335 7 m0∑ m0∑ PROPN ejpam-6732 335 8 k=0 k=0 PROPN ejpam-6732 335 9 2kα∞u 2kα∞u NUM ejpam-6732 335 10 ( ( PUNCT ejpam-6732 335 11 ∞∑ ∞∑ NUM ejpam-6732 335 12 i i PROPN ejpam-6732 335 13 = = PROPN ejpam-6732 335 14 k k NOUN ejpam-6732 335 15 |λi| |λi| NOUN ejpam-6732 335 16 2−kn2−iv2k(v+ 2−kn2−iv2k(v+ NUM ejpam-6732 335 17 n n NOUN ejpam-6732 335 18 s s PART ejpam-6732 335 19 ) ) PUNCT ejpam-6732 335 20 ∥χbk ∥χbk NUM ejpam-6732 335 21 ∥q1 ∥q1 NOUN ejpam-6732 335 22 ( ( PUNCT ejpam-6732 335 23 · · PUNCT ejpam-6732 335 24 ) ) PUNCT ejpam-6732 335 25 ∥χbi∥q1 ∥χbi∥q1 PROPN ejpam-6732 335 26 ( ( PUNCT ejpam-6732 335 27 · · PUNCT ejpam-6732 335 28 ) ) PUNCT ejpam-6732 335 29 ( ( PUNCT ejpam-6732 335 30 k k NOUN ejpam-6732 335 31 − − PROPN ejpam-6732 335 32 i)m2−αii i)m2−αii NOUN ejpam-6732 335 33 ) ) PUNCT ejpam-6732 335 34 u u PROPN ejpam-6732 335 35 ≲ ≲ PROPN ejpam-6732 335 36 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 335 37 sup sup NOUN ejpam-6732 335 38 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 335 39 2−m0γu 2−m0γu NUM ejpam-6732 335 40 m0∑ m0∑ PROPN ejpam-6732 335 41 k=0 k=0 PROPN ejpam-6732 336 1 ∞∑ ∞∑ NUM ejpam-6732 336 2 i i PROPN ejpam-6732 336 3 = = PROPN ejpam-6732 336 4 k k X ejpam-6732 336 5 |λi|u |λi|u NOUN ejpam-6732 336 6 2v2(k−i)u(k 2v2(k−i)u(k NUM ejpam-6732 336 7 − − PROPN ejpam-6732 336 8 i)mu i)mu PROPN ejpam-6732 336 9 ≲ ≲ PROPN ejpam-6732 336 10 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 336 11 sup sup NOUN ejpam-6732 336 12 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 336 13 2−m0γu 2−m0γu NUM ejpam-6732 336 14 m0∑ m0∑ PROPN ejpam-6732 336 15 k=0 k=0 PROPN ejpam-6732 336 16 ( ( PUNCT ejpam-6732 336 17 ∞∑ ∞∑ NUM ejpam-6732 336 18 i i PROPN ejpam-6732 336 19 = = NOUN ejpam-6732 336 20 k k X ejpam-6732 336 21 |λi|u |λi|u NOUN ejpam-6732 336 22 2v2(i−k)u/2 2v2(i−k)u/2 ADJ ejpam-6732 336 23 ) ) PUNCT ejpam-6732 336 24 × × NOUN ejpam-6732 336 25 ( ( PUNCT ejpam-6732 336 26 ∞∑ ∞∑ NUM ejpam-6732 336 27 i i PROPN ejpam-6732 336 28 = = NOUN ejpam-6732 336 29 k k PROPN ejpam-6732 336 30 2α(0)(k−i)u′/2(k 2α(0)(k−i)u′/2(k NOUN ejpam-6732 336 31 − − PROPN ejpam-6732 336 32 i)mu′/2 i)mu′/2 NOUN ejpam-6732 336 33 ) ) PUNCT ejpam-6732 336 34 u u NOUN ejpam-6732 336 35 / / SYM ejpam-6732 336 36 u′ u′ PROPN ejpam-6732 336 37 ≲ ≲ PROPN ejpam-6732 336 38 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 336 39 sup sup NOUN ejpam-6732 336 40 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 336 41 2−m0γu 2−m0γu NUM ejpam-6732 336 42 m0∑ m0∑ PROPN ejpam-6732 336 43 k=0 k=0 PROPN ejpam-6732 336 44 ( ( PUNCT ejpam-6732 336 45 ∞∑ ∞∑ NUM ejpam-6732 336 46 i i PROPN ejpam-6732 336 47 = = NOUN ejpam-6732 336 48 k k X ejpam-6732 336 49 |λi|u |λi|u NOUN ejpam-6732 336 50 2v2(i−k)u/2 2v2(i−k)u/2 ADJ ejpam-6732 336 51 ) ) PUNCT ejpam-6732 337 1 ≲ ≲ PROPN ejpam-6732 337 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 337 3 sup sup NOUN ejpam-6732 337 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 337 5 2−m0γu 2−m0γu NUM ejpam-6732 337 6 −1∑ −1∑ PROPN ejpam-6732 337 7 i=−∞ i=−∞ NOUN ejpam-6732 337 8 |λi|u |λi|u NOUN ejpam-6732 337 9 i∑ i∑ PROPN ejpam-6732 337 10 k=−∞ k=−∞ PROPN ejpam-6732 337 11 2v2(i−k)u/2 2v2(i−k)u/2 PROPN ejpam-6732 337 12 b. b. PROPN ejpam-6732 337 13 sultan sultan PROPN ejpam-6732 337 14 et et PROPN ejpam-6732 337 15 al al PROPN ejpam-6732 337 16 . . PUNCT ejpam-6732 337 17 / / SYM ejpam-6732 337 18 eur eur PROPN ejpam-6732 337 19 . . PUNCT ejpam-6732 338 1 j. j. PROPN ejpam-6732 338 2 pure pure PROPN ejpam-6732 338 3 appl appl PROPN ejpam-6732 338 4 . . PROPN ejpam-6732 338 5 math math PROPN ejpam-6732 338 6 , , PUNCT ejpam-6732 338 7 18 18 NUM ejpam-6732 338 8 ( ( PUNCT ejpam-6732 338 9 4 4 NUM ejpam-6732 338 10 ) ) PUNCT ejpam-6732 338 11 ( ( PUNCT ejpam-6732 338 12 2025 2025 NUM ejpam-6732 338 13 ) ) PUNCT ejpam-6732 338 14 , , PUNCT ejpam-6732 338 15 6732 6732 NUM ejpam-6732 338 16 16 16 NUM ejpam-6732 338 17 of of ADP ejpam-6732 338 18 20 20 NUM ejpam-6732 338 19 ≲ ≲ PROPN ejpam-6732 338 20 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 338 21 sup sup NOUN ejpam-6732 338 22 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 338 23 2−m0γu 2−m0γu NUM ejpam-6732 338 24 ∞∑ ∞∑ PRON ejpam-6732 338 25 i=0 i=0 ADJ ejpam-6732 338 26 |λi|u |λi|u NOUN ejpam-6732 338 27 i∑ i∑ ADJ ejpam-6732 338 28 k=0 k=0 PROPN ejpam-6732 338 29 2v2(k−i)u/2 2v2(k−i)u/2 ADJ ejpam-6732 338 30 ≲ ≲ PROPN ejpam-6732 338 31 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 338 32 λ λ PROPN ejpam-6732 338 33 . . PROPN ejpam-6732 339 1 next next ADV ejpam-6732 339 2 we we PRON ejpam-6732 339 3 have have VERB ejpam-6732 339 4 iii2 iii2 NOUN ejpam-6732 339 5 = = NOUN ejpam-6732 339 6 sup sup NOUN ejpam-6732 339 7 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 339 8 2−m0γu 2−m0γu NUM ejpam-6732 339 9 m0∑ m0∑ PROPN ejpam-6732 339 10 k=0 k=0 PROPN ejpam-6732 339 11 2kα∞u 2kα∞u NUM ejpam-6732 339 12 ( ( PUNCT ejpam-6732 339 13 k−1∑ k−1∑ PROPN ejpam-6732 339 14 i=−∞ i=−∞ NUM ejpam-6732 339 15 |λi| |λi| NOUN ejpam-6732 339 16 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 339 17 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 339 18 ) ) PUNCT ejpam-6732 340 1 [ [ X ejpam-6732 340 2 b b X ejpam-6732 340 3 , , PUNCT ejpam-6732 340 4 µφ µφ PROPN ejpam-6732 340 5 ] ] X ejpam-6732 340 6 m m VERB ejpam-6732 340 7 β β X ejpam-6732 340 8 bi bi NOUN ejpam-6732 340 9 ) ) PUNCT ejpam-6732 340 10 χk χk PROPN ejpam-6732 340 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 340 12 q2 q2 NOUN ejpam-6732 340 13 ( ( PUNCT ejpam-6732 340 14 · · PUNCT ejpam-6732 340 15 ) ) PUNCT ejpam-6732 340 16 ) ) PUNCT ejpam-6732 341 1 u u PRON ejpam-6732 341 2 ≲ ≲ PROPN ejpam-6732 341 3 sup sup NOUN ejpam-6732 341 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 341 5 2−m0γu 2−m0γu NUM ejpam-6732 341 6 m0∑ m0∑ PROPN ejpam-6732 341 7 k=0 k=0 PROPN ejpam-6732 341 8 2kα∞u 2kα∞u NUM ejpam-6732 341 9 ( ( PUNCT ejpam-6732 341 10 −1∑ −1∑ PROPN ejpam-6732 341 11 i=−∞ i=−∞ NOUN ejpam-6732 341 12 |λi| |λi| NOUN ejpam-6732 341 13 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 341 14 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 341 15 ) ) PUNCT ejpam-6732 342 1 [ [ X ejpam-6732 342 2 b b X ejpam-6732 342 3 , , PUNCT ejpam-6732 342 4 µφ µφ PROPN ejpam-6732 342 5 ] ] X ejpam-6732 342 6 m m VERB ejpam-6732 342 7 β β X ejpam-6732 342 8 bi bi NOUN ejpam-6732 342 9 ) ) PUNCT ejpam-6732 342 10 χk χk PROPN ejpam-6732 342 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 342 12 q2 q2 NOUN ejpam-6732 342 13 ( ( PUNCT ejpam-6732 342 14 · · PUNCT ejpam-6732 342 15 ) ) PUNCT ejpam-6732 342 16 ) ) PUNCT ejpam-6732 342 17 u u NOUN ejpam-6732 342 18 + + NOUN ejpam-6732 342 19 sup sup PROPN ejpam-6732 342 20 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 342 21 2−m0γu 2−m0γu NUM ejpam-6732 342 22 m0∑ m0∑ PROPN ejpam-6732 342 23 k=0 k=0 PROPN ejpam-6732 342 24 2kα∞u 2kα∞u NUM ejpam-6732 342 25 ( ( PUNCT ejpam-6732 342 26 k−1∑ k−1∑ PROPN ejpam-6732 342 27 i=0 i=0 PROPN ejpam-6732 342 28 |λi| |λi| PROPN ejpam-6732 342 29 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 342 30 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 342 31 ) ) PUNCT ejpam-6732 343 1 [ [ X ejpam-6732 343 2 b b X ejpam-6732 343 3 , , PUNCT ejpam-6732 343 4 µφ µφ PROPN ejpam-6732 343 5 ] ] X ejpam-6732 343 6 m m VERB ejpam-6732 343 7 β β X ejpam-6732 343 8 bi bi NOUN ejpam-6732 343 9 ) ) PUNCT ejpam-6732 343 10 χk χk PROPN ejpam-6732 343 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 343 12 q2 q2 NOUN ejpam-6732 343 13 ( ( PUNCT ejpam-6732 343 14 · · PUNCT ejpam-6732 343 15 ) ) PUNCT ejpam-6732 343 16 ) ) PUNCT ejpam-6732 343 17 u u NOUN ejpam-6732 343 18 ≲iii12 ≲iii12 NOUN ejpam-6732 343 19 + + CCONJ ejpam-6732 343 20 iii22 iii22 PROPN ejpam-6732 343 21 . . PUNCT ejpam-6732 344 1 estimate estimate NOUN ejpam-6732 344 2 of of ADP ejpam-6732 344 3 second second ADJ ejpam-6732 344 4 term term NOUN ejpam-6732 344 5 is be AUX ejpam-6732 344 6 essentially essentially ADV ejpam-6732 344 7 similar similar ADJ ejpam-6732 344 8 to to ADP ejpam-6732 344 9 iii1 iii1 PROPN ejpam-6732 344 10 . . PUNCT ejpam-6732 345 1 for for ADP ejpam-6732 345 2 iii iii NUM ejpam-6732 345 3 1 1 NUM ejpam-6732 345 4 2 2 NUM ejpam-6732 345 5 , , PUNCT ejpam-6732 345 6 we we PRON ejpam-6732 345 7 have have VERB ejpam-6732 345 8 ∥(1 ∥(1 NOUN ejpam-6732 345 9 + + CCONJ ejpam-6732 345 10 |z1|)−λ(z1 |z1|)−λ(z1 NOUN ejpam-6732 345 11 ) ) PUNCT ejpam-6732 346 1 [ [ X ejpam-6732 346 2 b b X ejpam-6732 346 3 , , PUNCT ejpam-6732 346 4 µφ µφ PROPN ejpam-6732 346 5 ] ] X ejpam-6732 346 6 m m VERB ejpam-6732 346 7 β β NOUN ejpam-6732 346 8 biχk∥q2 biχk∥q2 PROPN ejpam-6732 346 9 ( ( PUNCT ejpam-6732 346 10 · · PUNCT ejpam-6732 346 11 ) ) PUNCT ejpam-6732 346 12 ≤c(k ≤c(k NOUN ejpam-6732 346 13 − − NOUN ejpam-6732 346 14 i)m i)m NOUN ejpam-6732 346 15 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 ADJ ejpam-6732 346 16 ) ) PUNCT ejpam-6732 346 17 ∥f∥ ∥f∥ PROPN ejpam-6732 346 18 m m PROPN ejpam-6732 346 19 bmo bmo NOUN ejpam-6732 346 20 2−kn2−iv2k(v+ 2−kn2−iv2k(v+ NUM ejpam-6732 346 21 n n X ejpam-6732 346 22 s s PART ejpam-6732 346 23 ) ) PUNCT ejpam-6732 346 24 ∥χbk ∥χbk NUM ejpam-6732 346 25 ∥q1 ∥q1 NOUN ejpam-6732 346 26 ( ( PUNCT ejpam-6732 346 27 · · PUNCT ejpam-6732 346 28 ) ) PUNCT ejpam-6732 346 29 ∥χdl ∥χdl PROPN ejpam-6732 346 30 ∥q1 ∥q1 NOUN ejpam-6732 346 31 ( ( PUNCT ejpam-6732 346 32 · · PUNCT ejpam-6732 346 33 ) ) PUNCT ejpam-6732 346 34 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 346 35 ( ( PUNCT ejpam-6732 346 36 · · PUNCT ejpam-6732 346 37 ) ) PUNCT ejpam-6732 346 38 ≤c(k ≤c(k NOUN ejpam-6732 346 39 − − NOUN ejpam-6732 346 40 i)m i)m NOUN ejpam-6732 346 41 ∥φ∥ls(sn−1 ∥φ∥ls(sn−1 ADJ ejpam-6732 346 42 ) ) PUNCT ejpam-6732 346 43 ∥f∥ ∥f∥ PROPN ejpam-6732 346 44 m m PROPN ejpam-6732 346 45 bmo bmo NOUN ejpam-6732 346 46 2 2 NUM ejpam-6732 346 47 i i PROPN ejpam-6732 346 48 ( ( PUNCT ejpam-6732 346 49 n n X ejpam-6732 346 50 q1(0 q1(0 PROPN ejpam-6732 346 51 ) ) PUNCT ejpam-6732 346 52 −v −v NOUN ejpam-6732 346 53 ) ) PUNCT ejpam-6732 346 54 2 2 NUM ejpam-6732 346 55 k(v+n k(v+n NOUN ejpam-6732 346 56 s s PART ejpam-6732 346 57 − − PROPN ejpam-6732 346 58 n n CCONJ ejpam-6732 346 59 q′1∞ q′1∞ NOUN ejpam-6732 346 60 ) ) PUNCT ejpam-6732 346 61 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 346 62 ( ( PUNCT ejpam-6732 346 63 · · PUNCT ejpam-6732 346 64 ) ) PUNCT ejpam-6732 346 65 . . PUNCT ejpam-6732 347 1 when when SCONJ ejpam-6732 347 2 0 0 NUM ejpam-6732 347 3 < < X ejpam-6732 347 4 u u X ejpam-6732 347 5 ≤ ≤ NOUN ejpam-6732 347 6 1 1 NUM ejpam-6732 347 7 , , PUNCT ejpam-6732 347 8 we we PRON ejpam-6732 347 9 have have VERB ejpam-6732 347 10 iii12 iii12 NOUN ejpam-6732 348 1 = = NOUN ejpam-6732 348 2 sup sup NOUN ejpam-6732 348 3 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 348 4 2−m0γu 2−m0γu NUM ejpam-6732 348 5 m0∑ m0∑ PROPN ejpam-6732 348 6 k=0 k=0 PROPN ejpam-6732 348 7 2α∞ku 2α∞ku PROPN ejpam-6732 348 8 ( ( PUNCT ejpam-6732 348 9 −1∑ −1∑ PROPN ejpam-6732 348 10 i=−∞ i=−∞ NOUN ejpam-6732 348 11 |λi| |λi| NOUN ejpam-6732 348 12 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 348 13 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 348 14 ) ) PUNCT ejpam-6732 349 1 [ [ X ejpam-6732 349 2 b b X ejpam-6732 349 3 , , PUNCT ejpam-6732 349 4 µφ µφ PROPN ejpam-6732 349 5 ] ] X ejpam-6732 349 6 m m VERB ejpam-6732 349 7 β β X ejpam-6732 349 8 bi bi NOUN ejpam-6732 349 9 ) ) PUNCT ejpam-6732 349 10 χk χk PROPN ejpam-6732 349 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 349 12 q2 q2 NOUN ejpam-6732 349 13 ( ( PUNCT ejpam-6732 349 14 · · PUNCT ejpam-6732 349 15 ) ) PUNCT ejpam-6732 349 16 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 349 17 ( ( PUNCT ejpam-6732 349 18 · · PUNCT ejpam-6732 349 19 ) ) PUNCT ejpam-6732 349 20 ) ) PUNCT ejpam-6732 350 1 u u PROPN ejpam-6732 350 2 ≲ ≲ PROPN ejpam-6732 350 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 350 4 sup sup NOUN ejpam-6732 350 5 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 350 6 2−m0γu 2−m0γu NUM ejpam-6732 350 7 m0∑ m0∑ PROPN ejpam-6732 350 8 k=0 k=0 PROPN ejpam-6732 350 9 2α∞ku 2α∞ku PROPN ejpam-6732 350 10 ( ( PUNCT ejpam-6732 350 11 −1∑ −1∑ PROPN ejpam-6732 350 12 i=−∞ i=−∞ NOUN ejpam-6732 350 13 |λi|u |λi|u NOUN ejpam-6732 350 14 ( ( PUNCT ejpam-6732 350 15 k k PROPN ejpam-6732 350 16 − − PROPN ejpam-6732 350 17 i)mu2 i)mu2 X ejpam-6732 350 18 lu lu PROPN ejpam-6732 350 19 ( ( PUNCT ejpam-6732 350 20 n n X ejpam-6732 350 21 q1(0 q1(0 PROPN ejpam-6732 350 22 ) ) PUNCT ejpam-6732 350 23 −v −v NOUN ejpam-6732 350 24 ) ) PUNCT ejpam-6732 350 25 2 2 NUM ejpam-6732 350 26 ku(v+n ku(v+n NOUN ejpam-6732 350 27 s s PART ejpam-6732 350 28 − − PROPN ejpam-6732 350 29 n n CCONJ ejpam-6732 350 30 q′1∞ q′1∞ NOUN ejpam-6732 350 31 ) ) PUNCT ejpam-6732 350 32 ∥bi∥uq1 ∥bi∥uq1 PROPN ejpam-6732 350 33 ( ( PUNCT ejpam-6732 350 34 · · PUNCT ejpam-6732 350 35 ) ) PUNCT ejpam-6732 350 36 ) ) PUNCT ejpam-6732 351 1 = = SYM ejpam-6732 351 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 351 3 sup sup NOUN ejpam-6732 351 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 351 5 2−m0γu 2−m0γu NUM ejpam-6732 351 6 × × NOUN ejpam-6732 351 7 m0∑ m0∑ PROPN ejpam-6732 351 8 k=0 k=0 PROPN ejpam-6732 351 9 2α∞ku 2α∞ku PROPN ejpam-6732 351 10 ( ( PUNCT ejpam-6732 351 11 −1∑ −1∑ PROPN ejpam-6732 351 12 i=−∞ i=−∞ NOUN ejpam-6732 351 13 |λi|u |λi|u NOUN ejpam-6732 351 14 ( ( PUNCT ejpam-6732 351 15 k k PROPN ejpam-6732 351 16 − − PROPN ejpam-6732 351 17 i)mu2 i)mu2 X ejpam-6732 351 18 lu lu PROPN ejpam-6732 351 19 ( ( PUNCT ejpam-6732 351 20 n n X ejpam-6732 351 21 q1(0 q1(0 PROPN ejpam-6732 351 22 ) ) PUNCT ejpam-6732 351 23 −v−α∞ −v−α∞ NUM ejpam-6732 351 24 ) ) PUNCT ejpam-6732 351 25 2 2 NUM ejpam-6732 351 26 ku(v+n ku(v+n NOUN ejpam-6732 351 27 s s PART ejpam-6732 351 28 − − PROPN ejpam-6732 351 29 n n PRON ejpam-6732 351 30 q′1∞ q′1∞ NOUN ejpam-6732 351 31 ) ) PUNCT ejpam-6732 351 32 ) ) PUNCT ejpam-6732 352 1 ≲ ≲ PROPN ejpam-6732 352 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 352 3 sup sup NOUN ejpam-6732 352 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 352 5 2−m0γu 2−m0γu NUM ejpam-6732 352 6 m0∑ m0∑ PROPN ejpam-6732 352 7 k=0 k=0 PROPN ejpam-6732 352 8 2 2 NUM ejpam-6732 352 9 ku(v+n ku(v+n NOUN ejpam-6732 352 10 s s PART ejpam-6732 352 11 − − PROPN ejpam-6732 352 12 n n CCONJ ejpam-6732 352 13 q′1∞ q′1∞ NOUN ejpam-6732 352 14 ) ) PUNCT ejpam-6732 353 1 ( ( PUNCT ejpam-6732 353 2 k k X ejpam-6732 353 3 − − PROPN ejpam-6732 353 4 i)mu i)mu PROPN ejpam-6732 353 5 −1∑ −1∑ PROPN ejpam-6732 353 6 i=−∞ i=−∞ NOUN ejpam-6732 353 7 |λi|u |λi|u NOUN ejpam-6732 353 8 2 2 NUM ejpam-6732 353 9 lu lu PROPN ejpam-6732 353 10 ( ( PUNCT ejpam-6732 353 11 n n X ejpam-6732 353 12 q1(0 q1(0 PROPN ejpam-6732 353 13 ) ) PUNCT ejpam-6732 353 14 −v−α∞ −v−α∞ NUM ejpam-6732 353 15 ) ) PUNCT ejpam-6732 354 1 ≲ ≲ PROPN ejpam-6732 354 2 ∥f∥mbmo ∥f∥mbmo NUM ejpam-6732 354 3 sup sup NOUN ejpam-6732 354 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 354 5 2−m0γu 2−m0γu NUM ejpam-6732 354 6 −1∑ −1∑ PROPN ejpam-6732 354 7 i=−∞ i=−∞ NOUN ejpam-6732 354 8 |λi|u |λi|u PROPN ejpam-6732 354 9 b. b. PROPN ejpam-6732 354 10 sultan sultan PROPN ejpam-6732 354 11 et et PROPN ejpam-6732 355 1 al al PROPN ejpam-6732 355 2 . . PUNCT ejpam-6732 355 3 / / SYM ejpam-6732 355 4 eur eur PROPN ejpam-6732 355 5 . . PUNCT ejpam-6732 356 1 j. j. PROPN ejpam-6732 356 2 pure pure PROPN ejpam-6732 356 3 appl appl PROPN ejpam-6732 356 4 . . PROPN ejpam-6732 356 5 math math PROPN ejpam-6732 356 6 , , PUNCT ejpam-6732 356 7 18 18 NUM ejpam-6732 356 8 ( ( PUNCT ejpam-6732 356 9 4 4 NUM ejpam-6732 356 10 ) ) PUNCT ejpam-6732 356 11 ( ( PUNCT ejpam-6732 356 12 2025 2025 NUM ejpam-6732 356 13 ) ) PUNCT ejpam-6732 356 14 , , PUNCT ejpam-6732 356 15 6732 6732 NUM ejpam-6732 356 16 17 17 NUM ejpam-6732 356 17 of of ADP ejpam-6732 356 18 20 20 NUM ejpam-6732 356 19 ≲ ≲ PROPN ejpam-6732 356 20 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 356 21 λ λ PROPN ejpam-6732 356 22 . . PUNCT ejpam-6732 357 1 when when SCONJ ejpam-6732 357 2 1 1 NUM ejpam-6732 357 3 < < X ejpam-6732 357 4 u u X ejpam-6732 357 5 < < X ejpam-6732 357 6 ∞ ∞ PROPN ejpam-6732 357 7 , , PUNCT ejpam-6732 357 8 we we PRON ejpam-6732 357 9 have have VERB ejpam-6732 357 10 iii12 iii12 NOUN ejpam-6732 358 1 = = NOUN ejpam-6732 358 2 sup sup NOUN ejpam-6732 358 3 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 358 4 2−m0γu 2−m0γu NUM ejpam-6732 358 5 m0∑ m0∑ PROPN ejpam-6732 358 6 k=0 k=0 PROPN ejpam-6732 358 7 2α∞ku 2α∞ku PROPN ejpam-6732 358 8 ( ( PUNCT ejpam-6732 358 9 −1∑ −1∑ PROPN ejpam-6732 358 10 i=−∞ i=−∞ NOUN ejpam-6732 358 11 |λi| |λi| NOUN ejpam-6732 358 12 ∥∥∥((|z1|+ ∥∥∥((|z1|+ NOUN ejpam-6732 358 13 1)−λ(z1 1)−λ(z1 NUM ejpam-6732 358 14 ) ) PUNCT ejpam-6732 359 1 [ [ X ejpam-6732 359 2 b b X ejpam-6732 359 3 , , PUNCT ejpam-6732 359 4 µφ µφ PROPN ejpam-6732 359 5 ] ] X ejpam-6732 359 6 m m VERB ejpam-6732 359 7 β β X ejpam-6732 359 8 bi bi NOUN ejpam-6732 359 9 ) ) PUNCT ejpam-6732 359 10 χk χk PROPN ejpam-6732 359 11 ∥∥∥ ∥∥∥ PROPN ejpam-6732 359 12 q2 q2 NOUN ejpam-6732 359 13 ( ( PUNCT ejpam-6732 359 14 · · PUNCT ejpam-6732 359 15 ) ) PUNCT ejpam-6732 359 16 ∥bi∥q1 ∥bi∥q1 PROPN ejpam-6732 359 17 ( ( PUNCT ejpam-6732 359 18 · · PUNCT ejpam-6732 359 19 ) ) PUNCT ejpam-6732 359 20 ) ) PUNCT ejpam-6732 360 1 u u PROPN ejpam-6732 360 2 ≲ ≲ PROPN ejpam-6732 360 3 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 360 4 sup sup NOUN ejpam-6732 360 5 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 360 6 2−m0γu 2−m0γu NUM ejpam-6732 360 7 m0∑ m0∑ PROPN ejpam-6732 360 8 k=0 k=0 PROPN ejpam-6732 360 9 2α∞ku 2α∞ku PROPN ejpam-6732 360 10 ( ( PUNCT ejpam-6732 360 11 −1∑ −1∑ PROPN ejpam-6732 360 12 i=−∞ i=−∞ NOUN ejpam-6732 360 13 |λi|u |λi|u NOUN ejpam-6732 360 14 ( ( PUNCT ejpam-6732 360 15 k k PROPN ejpam-6732 360 16 − − PROPN ejpam-6732 360 17 i)mu2 i)mu2 X ejpam-6732 360 18 lu lu PROPN ejpam-6732 360 19 ( ( PUNCT ejpam-6732 360 20 n n X ejpam-6732 360 21 q1(0 q1(0 PROPN ejpam-6732 360 22 ) ) PUNCT ejpam-6732 360 23 −v −v NOUN ejpam-6732 360 24 ) ) PUNCT ejpam-6732 360 25 2 2 NUM ejpam-6732 360 26 ku(v+n ku(v+n NOUN ejpam-6732 360 27 s s PART ejpam-6732 360 28 − − PROPN ejpam-6732 360 29 n n CCONJ ejpam-6732 360 30 q′1∞ q′1∞ NOUN ejpam-6732 360 31 ) ) PUNCT ejpam-6732 360 32 ∥bi∥uq1 ∥bi∥uq1 PROPN ejpam-6732 360 33 ( ( PUNCT ejpam-6732 360 34 · · PUNCT ejpam-6732 360 35 ) ) PUNCT ejpam-6732 360 36 ) ) PUNCT ejpam-6732 361 1 ≲ ≲ PROPN ejpam-6732 361 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 361 3 sup sup NOUN ejpam-6732 361 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 361 5 2−m0γu 2−m0γu NUM ejpam-6732 361 6 m0∑ m0∑ PROPN ejpam-6732 361 7 k=0 k=0 PROPN ejpam-6732 361 8 2α∞ku2 2α∞ku2 NUM ejpam-6732 361 9 ku(v+n ku(v+n PROPN ejpam-6732 361 10 s s PART ejpam-6732 361 11 − − PROPN ejpam-6732 361 12 n n X ejpam-6732 361 13 q′1∞ q′1∞ NOUN ejpam-6732 361 14 ) ) PUNCT ejpam-6732 362 1 ( ( PUNCT ejpam-6732 362 2 −1∑ −1∑ PROPN ejpam-6732 362 3 i=−∞ i=−∞ NOUN ejpam-6732 362 4 |λi|u |λi|u NOUN ejpam-6732 362 5 ( ( PUNCT ejpam-6732 362 6 k k PROPN ejpam-6732 362 7 − − PROPN ejpam-6732 362 8 i)mu2 i)mu2 X ejpam-6732 362 9 lu lu PROPN ejpam-6732 362 10 ( ( PUNCT ejpam-6732 362 11 n n X ejpam-6732 362 12 q1(0 q1(0 PROPN ejpam-6732 362 13 ) ) PUNCT ejpam-6732 362 14 −v−α(0 −v−α(0 PROPN ejpam-6732 362 15 ) ) PUNCT ejpam-6732 362 16 ) ) PUNCT ejpam-6732 362 17 ) ) PUNCT ejpam-6732 363 1 ≲ ≲ PROPN ejpam-6732 363 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 363 3 sup sup NOUN ejpam-6732 363 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 363 5 2−m0γu 2−m0γu NUM ejpam-6732 363 6 m0∑ m0∑ PROPN ejpam-6732 363 7 k=0 k=0 PROPN ejpam-6732 363 8 ( ( PUNCT ejpam-6732 363 9 −1∑ −1∑ PROPN ejpam-6732 363 10 i=−∞ i=−∞ NOUN ejpam-6732 363 11 |λi|u |λi|u NOUN ejpam-6732 363 12 ( ( PUNCT ejpam-6732 363 13 k k PROPN ejpam-6732 363 14 − − PROPN ejpam-6732 363 15 i)mu2 i)mu2 X ejpam-6732 363 16 lu lu PROPN ejpam-6732 363 17 ( ( PUNCT ejpam-6732 363 18 n n X ejpam-6732 363 19 q1(0 q1(0 PROPN ejpam-6732 363 20 ) ) PUNCT ejpam-6732 363 21 −v−α(0 −v−α(0 PROPN ejpam-6732 363 22 ) ) PUNCT ejpam-6732 363 23 ) ) PUNCT ejpam-6732 363 24 ) ) PUNCT ejpam-6732 364 1 ≲ ≲ PROPN ejpam-6732 364 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 364 3 sup sup NOUN ejpam-6732 364 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 364 5 2−m0γu 2−m0γu NUM ejpam-6732 364 6 m0∑ m0∑ PROPN ejpam-6732 364 7 k=0 k=0 PROPN ejpam-6732 364 8 ( ( PUNCT ejpam-6732 364 9 −1∑ −1∑ PROPN ejpam-6732 364 10 i=0 i=0 PROPN ejpam-6732 364 11 |λi|u |λi|u NOUN ejpam-6732 364 12 2 2 NUM ejpam-6732 364 13 i i NOUN ejpam-6732 364 14 ( ( PUNCT ejpam-6732 364 15 n n X ejpam-6732 364 16 q1(0 q1(0 PROPN ejpam-6732 364 17 ) ) PUNCT ejpam-6732 364 18 −v−α(0))u/2 −v−α(0))u/2 ADV ejpam-6732 364 19 ) ) PUNCT ejpam-6732 364 20 × × NOUN ejpam-6732 364 21 ( ( PUNCT ejpam-6732 364 22 −1∑ −1∑ PROPN ejpam-6732 364 23 i=0 i=0 PROPN ejpam-6732 364 24 ( ( PUNCT ejpam-6732 364 25 k k NOUN ejpam-6732 364 26 − − PROPN ejpam-6732 364 27 i)mu′/22 i)mu′/22 PROPN ejpam-6732 365 1 i i PRON ejpam-6732 365 2 ( ( PUNCT ejpam-6732 365 3 n n X ejpam-6732 365 4 q1(0 q1(0 PROPN ejpam-6732 365 5 ) ) PUNCT ejpam-6732 365 6 −v−α(0))u′/2 −v−α(0))u′/2 NOUN ejpam-6732 365 7 ) ) PUNCT ejpam-6732 365 8 u/(u)′ u/(u)′ ADV ejpam-6732 365 9 ≲ ≲ PROPN ejpam-6732 365 10 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 365 11 sup sup NOUN ejpam-6732 365 12 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 365 13 2−m0γu 2−m0γu NUM ejpam-6732 365 14 m0∑ m0∑ PROPN ejpam-6732 365 15 k=0 k=0 PROPN ejpam-6732 365 16 ( ( PUNCT ejpam-6732 365 17 −1∑ −1∑ PROPN ejpam-6732 365 18 i=0 i=0 PROPN ejpam-6732 365 19 |λi|u |λi|u NOUN ejpam-6732 365 20 2 2 NUM ejpam-6732 365 21 i i NOUN ejpam-6732 365 22 ( ( PUNCT ejpam-6732 365 23 n n X ejpam-6732 365 24 q1(0 q1(0 PROPN ejpam-6732 365 25 ) ) PUNCT ejpam-6732 365 26 −v−α(0))u/2 −v−α(0))u/2 ADV ejpam-6732 365 27 ) ) PUNCT ejpam-6732 366 1 ≲ ≲ PROPN ejpam-6732 366 2 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 366 3 sup sup NOUN ejpam-6732 366 4 m0≥0,m0∈z m0≥0,m0∈z VERB ejpam-6732 366 5 2−m0γu 2−m0γu NUM ejpam-6732 366 6 −1∑ −1∑ NOUN ejpam-6732 366 7 i=−∞ i=−∞ NOUN ejpam-6732 366 8 |λi|u |λi|u ADP ejpam-6732 366 9 ≲ ≲ PROPN ejpam-6732 366 10 ∥f∥mbmo ∥f∥mbmo X ejpam-6732 366 11 λ λ NOUN ejpam-6732 366 12 . . PUNCT ejpam-6732 367 1 thus thus ADV ejpam-6732 367 2 proof proof NOUN ejpam-6732 367 3 of of ADP ejpam-6732 367 4 the the DET ejpam-6732 367 5 theorem theorem NOUN ejpam-6732 367 6 is be AUX ejpam-6732 367 7 completed complete VERB ejpam-6732 367 8 . . PUNCT ejpam-6732 368 1 conflict conflict NOUN ejpam-6732 368 2 of of ADP ejpam-6732 368 3 interest interest NOUN ejpam-6732 368 4 the the DET ejpam-6732 368 5 authors author NOUN ejpam-6732 368 6 declare declare VERB ejpam-6732 368 7 that that SCONJ ejpam-6732 368 8 they they PRON ejpam-6732 368 9 have have VERB ejpam-6732 368 10 no no DET ejpam-6732 368 11 known know VERB ejpam-6732 368 12 competing compete VERB ejpam-6732 368 13 financial financial ADJ ejpam-6732 368 14 interests interest NOUN ejpam-6732 368 15 or or CCONJ ejpam-6732 368 16 personal personal ADJ ejpam-6732 368 17 relationships relationship NOUN ejpam-6732 368 18 that that PRON ejpam-6732 368 19 could could AUX ejpam-6732 368 20 have have AUX ejpam-6732 368 21 appeared appear VERB ejpam-6732 368 22 to to PART ejpam-6732 368 23 influence influence VERB ejpam-6732 368 24 the the DET ejpam-6732 368 25 work work NOUN ejpam-6732 368 26 reported report VERB ejpam-6732 368 27 in in ADP ejpam-6732 368 28 this this DET ejpam-6732 368 29 paper paper NOUN ejpam-6732 368 30 . . PUNCT ejpam-6732 369 1 references reference NOUN ejpam-6732 369 2 [ [ X ejpam-6732 369 3 1 1 NUM ejpam-6732 369 4 ] ] PUNCT ejpam-6732 369 5 m. m. NOUN ejpam-6732 369 6 izuki izuki PROPN ejpam-6732 369 7 . . PUNCT ejpam-6732 370 1 boundedness boundedness PROPN ejpam-6732 370 2 of of ADP ejpam-6732 370 3 sublinear sublinear NOUN ejpam-6732 370 4 operators operator NOUN ejpam-6732 370 5 on on ADP ejpam-6732 370 6 herz herz PROPN ejpam-6732 370 7 spaces space NOUN ejpam-6732 370 8 with with ADP ejpam-6732 370 9 variable variable ADJ ejpam-6732 370 10 exponent exponent NOUN ejpam-6732 370 11 and and CCONJ ejpam-6732 370 12 application application NOUN ejpam-6732 370 13 to to ADP ejpam-6732 370 14 wavelet wavelet NOUN ejpam-6732 370 15 characterization characterization NOUN ejpam-6732 370 16 . . PUNCT ejpam-6732 371 1 analysis analysis NOUN ejpam-6732 371 2 mathematica mathematica PROPN ejpam-6732 371 3 , , PUNCT ejpam-6732 371 4 36:33–50 36:33–50 NUM ejpam-6732 371 5 , , PUNCT ejpam-6732 371 6 2010 2010 NUM ejpam-6732 371 7 . . PUNCT ejpam-6732 372 1 [ [ X ejpam-6732 372 2 2 2 NUM ejpam-6732 372 3 ] ] PUNCT ejpam-6732 372 4 a. a. PROPN ejpam-6732 372 5 almeida almeida PROPN ejpam-6732 372 6 and and CCONJ ejpam-6732 372 7 d. d. PROPN ejpam-6732 372 8 drihem drihem PROPN ejpam-6732 372 9 . . PUNCT ejpam-6732 373 1 maximal maximal ADJ ejpam-6732 373 2 , , PUNCT ejpam-6732 373 3 potential potential ADJ ejpam-6732 373 4 and and CCONJ ejpam-6732 373 5 singular singular ADJ ejpam-6732 373 6 type type NOUN ejpam-6732 373 7 operators operator NOUN ejpam-6732 373 8 on on ADP ejpam-6732 373 9 herz herz PROPN ejpam-6732 373 10 spaces space NOUN ejpam-6732 373 11 with with ADP ejpam-6732 373 12 variable variable ADJ ejpam-6732 373 13 exponents exponent NOUN ejpam-6732 373 14 . . PUNCT ejpam-6732 374 1 journal journal NOUN ejpam-6732 374 2 of of ADP ejpam-6732 374 3 mathematical mathematical ADJ ejpam-6732 374 4 analysis analysis NOUN ejpam-6732 374 5 and and CCONJ ejpam-6732 374 6 applications application NOUN ejpam-6732 374 7 , , PUNCT ejpam-6732 374 8 394(2):781–795 394(2):781–795 NUM ejpam-6732 374 9 , , PUNCT ejpam-6732 374 10 2012 2012 NUM ejpam-6732 374 11 . . PUNCT ejpam-6732 375 1 b. b. PROPN ejpam-6732 375 2 sultan sultan PROPN ejpam-6732 375 3 et et PROPN ejpam-6732 375 4 al al PROPN ejpam-6732 375 5 . . PUNCT ejpam-6732 375 6 / / SYM ejpam-6732 375 7 eur eur PROPN ejpam-6732 375 8 . . PUNCT ejpam-6732 376 1 j. j. PROPN ejpam-6732 376 2 pure pure PROPN ejpam-6732 376 3 appl appl PROPN ejpam-6732 376 4 . . PROPN ejpam-6732 376 5 math math PROPN ejpam-6732 376 6 , , PUNCT ejpam-6732 376 7 18 18 NUM ejpam-6732 376 8 ( ( PUNCT ejpam-6732 376 9 4 4 NUM ejpam-6732 376 10 ) ) PUNCT ejpam-6732 376 11 ( ( PUNCT ejpam-6732 376 12 2025 2025 NUM ejpam-6732 376 13 ) ) PUNCT ejpam-6732 376 14 , , PUNCT ejpam-6732 376 15 6732 6732 NUM ejpam-6732 376 16 18 18 NUM ejpam-6732 376 17 of of ADP ejpam-6732 376 18 20 20 NUM ejpam-6732 376 19 [ [ SYM ejpam-6732 376 20 3 3 NUM ejpam-6732 376 21 ] ] X ejpam-6732 376 22 b. b. PROPN ejpam-6732 376 23 sultan sultan PROPN ejpam-6732 376 24 and and CCONJ ejpam-6732 376 25 m. m. PROPN ejpam-6732 376 26 sultan sultan PROPN ejpam-6732 376 27 . . PUNCT ejpam-6732 377 1 boundedness boundedness NOUN ejpam-6732 377 2 of of ADP ejpam-6732 377 3 commutators commutator NOUN ejpam-6732 377 4 of of ADP ejpam-6732 377 5 rough rough ADJ ejpam-6732 377 6 hardy hardy ADJ ejpam-6732 377 7 operators operator NOUN ejpam-6732 377 8 on on ADP ejpam-6732 377 9 grand grand ADJ ejpam-6732 377 10 variable variable ADJ ejpam-6732 377 11 herz herz PROPN ejpam-6732 377 12 spaces space NOUN ejpam-6732 377 13 . . PUNCT ejpam-6732 378 1 forum forum PROPN ejpam-6732 378 2 mathematicum mathematicum PROPN ejpam-6732 378 3 , , PUNCT ejpam-6732 378 4 2023 2023 NUM ejpam-6732 378 5 . . PUNCT ejpam-6732 379 1 [ [ X ejpam-6732 379 2 4 4 X ejpam-6732 379 3 ] ] PUNCT ejpam-6732 379 4 b. b. PROPN ejpam-6732 379 5 sultan sultan PROPN ejpam-6732 379 6 , , PUNCT ejpam-6732 379 7 m. m. NOUN ejpam-6732 379 8 sultan sultan PROPN ejpam-6732 379 9 , , PUNCT ejpam-6732 379 10 and and CCONJ ejpam-6732 379 11 i. i. PROPN ejpam-6732 379 12 khan khan PROPN ejpam-6732 379 13 . . PUNCT ejpam-6732 380 1 on on ADP ejpam-6732 380 2 sobolev sobolev PROPN ejpam-6732 380 3 theorem theorem NOUN ejpam-6732 380 4 for for ADP ejpam-6732 380 5 higher high ADJ ejpam-6732 380 6 commutators commutator NOUN ejpam-6732 380 7 of of ADP ejpam-6732 380 8 fractional fractional ADJ ejpam-6732 380 9 integrals integral NOUN ejpam-6732 380 10 in in ADP ejpam-6732 380 11 grand grand ADJ ejpam-6732 380 12 variable variable ADJ ejpam-6732 380 13 herz herz PROPN ejpam-6732 380 14 spaces space NOUN ejpam-6732 380 15 . . PUNCT ejpam-6732 381 1 communications communication NOUN ejpam-6732 381 2 in in ADP ejpam-6732 381 3 nonlinear nonlinear ADJ ejpam-6732 381 4 science science NOUN ejpam-6732 381 5 and and CCONJ ejpam-6732 381 6 numerical numerical PROPN ejpam-6732 381 7 simulation simulation PROPN ejpam-6732 381 8 , , PUNCT ejpam-6732 381 9 126:107489 126:107489 NUM ejpam-6732 381 10 , , PUNCT ejpam-6732 381 11 2023 2023 NUM ejpam-6732 381 12 . . PUNCT ejpam-6732 382 1 [ [ X ejpam-6732 382 2 5 5 NUM ejpam-6732 382 3 ] ] PUNCT ejpam-6732 382 4 a. a. NOUN ejpam-6732 382 5 hussain hussain PROPN ejpam-6732 382 6 , , PUNCT ejpam-6732 382 7 naqash naqash PROPN ejpam-6732 382 8 sarfraz sarfraz PROPN ejpam-6732 382 9 , , PUNCT ejpam-6732 382 10 and and CCONJ ejpam-6732 382 11 f. f. PROPN ejpam-6732 382 12 gurbuz gurbuz PROPN ejpam-6732 382 13 . . PUNCT ejpam-6732 383 1 sharp sharp ADJ ejpam-6732 383 2 weak weak ADJ ejpam-6732 383 3 bounds bound NOUN ejpam-6732 383 4 for for ADP ejpam-6732 383 5 p p NOUN ejpam-6732 383 6 - - PUNCT ejpam-6732 383 7 adic adic ADJ ejpam-6732 383 8 hardy hardy ADJ ejpam-6732 383 9 operators operator NOUN ejpam-6732 383 10 on on ADP ejpam-6732 383 11 p p ADJ ejpam-6732 383 12 - - PUNCT ejpam-6732 383 13 adic adic ADJ ejpam-6732 383 14 linear linear ADJ ejpam-6732 383 15 spaces space NOUN ejpam-6732 383 16 . . PUNCT ejpam-6732 384 1 commun commun PROPN ejpam-6732 384 2 . . PUNCT ejpam-6732 385 1 fac fac PROPN ejpam-6732 385 2 . . PUNCT ejpam-6732 385 3 sci sci PROPN ejpam-6732 385 4 . . PROPN ejpam-6732 385 5 univ univ PROPN ejpam-6732 385 6 . . PUNCT ejpam-6732 386 1 ank ank PROPN ejpam-6732 386 2 . . PROPN ejpam-6732 386 3 ser ser PROPN ejpam-6732 386 4 . . PUNCT ejpam-6732 387 1 a1 a1 NOUN ejpam-6732 387 2 math math NOUN ejpam-6732 387 3 . . PUNCT ejpam-6732 388 1 stat stat PROPN ejpam-6732 388 2 . . PUNCT ejpam-6732 388 3 , , PUNCT ejpam-6732 388 4 71(4):919–929 71(4):919–929 NOUN ejpam-6732 388 5 , , PUNCT ejpam-6732 388 6 2022 2022 NUM ejpam-6732 388 7 . . PUNCT ejpam-6732 389 1 [ [ X ejpam-6732 389 2 6 6 NUM ejpam-6732 389 3 ] ] PUNCT ejpam-6732 389 4 a. a. NOUN ejpam-6732 389 5 hussain hussain PROPN ejpam-6732 389 6 , , PUNCT ejpam-6732 389 7 n. n. PROPN ejpam-6732 389 8 sarfraz sarfraz PROPN ejpam-6732 389 9 , , PUNCT ejpam-6732 389 10 et et PROPN ejpam-6732 389 11 al al PROPN ejpam-6732 389 12 . . PUNCT ejpam-6732 390 1 the the DET ejpam-6732 390 2 boundedness boundedness NOUN ejpam-6732 390 3 of of ADP ejpam-6732 390 4 commutators commutator NOUN ejpam-6732 390 5 of of ADP ejpam-6732 390 6 rough rough ADJ ejpam-6732 390 7 p p ADJ ejpam-6732 390 8 - - PUNCT ejpam-6732 390 9 adic adic ADJ ejpam-6732 390 10 fractional fractional ADJ ejpam-6732 390 11 hardy hardy ADJ ejpam-6732 390 12 type type NOUN ejpam-6732 390 13 operators operator NOUN ejpam-6732 390 14 on on ADP ejpam-6732 390 15 herz herz ADJ ejpam-6732 390 16 - - PUNCT ejpam-6732 390 17 type type NOUN ejpam-6732 390 18 spaces space NOUN ejpam-6732 390 19 . . PUNCT ejpam-6732 391 1 j. j. PROPN ejpam-6732 391 2 inequal inequal PROPN ejpam-6732 391 3 . . PUNCT ejpam-6732 392 1 appl appl PROPN ejpam-6732 392 2 . . PROPN ejpam-6732 392 3 , , PUNCT ejpam-6732 392 4 2021:123 2021:123 NUM ejpam-6732 392 5 , , PUNCT ejpam-6732 392 6 2021 2021 NUM ejpam-6732 392 7 . . PUNCT ejpam-6732 393 1 article article NOUN ejpam-6732 393 2 i i PROPN ejpam-6732 393 3 d d PROPN ejpam-6732 393 4 123 123 NUM ejpam-6732 393 5 . . PUNCT ejpam-6732 394 1 [ [ X ejpam-6732 394 2 7 7 X ejpam-6732 394 3 ] ] PUNCT ejpam-6732 394 4 a. a. NOUN ejpam-6732 394 5 hussain hussain PROPN ejpam-6732 394 6 , , PUNCT ejpam-6732 394 7 n. n. PROPN ejpam-6732 394 8 sarfraz sarfraz PROPN ejpam-6732 394 9 , , PUNCT ejpam-6732 394 10 ilyas ilyas PROPN ejpam-6732 394 11 khan khan PROPN ejpam-6732 394 12 , , PUNCT ejpam-6732 394 13 and and CCONJ ejpam-6732 394 14 a. a. NOUN ejpam-6732 394 15 m. m. PROPN ejpam-6732 394 16 alqahtani alqahtani PROPN ejpam-6732 394 17 . . PUNCT ejpam-6732 395 1 estimates estimate NOUN ejpam-6732 395 2 for for ADP ejpam-6732 395 3 commutators commutator NOUN ejpam-6732 395 4 of of ADP ejpam-6732 395 5 bilinear bilinear NOUN ejpam-6732 395 6 fractional fractional ADJ ejpam-6732 395 7 p p NOUN ejpam-6732 395 8 - - PUNCT ejpam-6732 395 9 adic adic ADJ ejpam-6732 395 10 hardy hardy ADJ ejpam-6732 395 11 operator operator NOUN ejpam-6732 395 12 on on ADP ejpam-6732 395 13 herz herz ADJ ejpam-6732 395 14 - - PUNCT ejpam-6732 395 15 type type NOUN ejpam-6732 395 16 spaces space NOUN ejpam-6732 395 17 . . PUNCT ejpam-6732 396 1 j. j. PROPN ejpam-6732 396 2 funct funct PROPN ejpam-6732 396 3 . . PUNCT ejpam-6732 397 1 spaces space NOUN ejpam-6732 397 2 , , PUNCT ejpam-6732 397 3 2021:6615604 2021:6615604 NUM ejpam-6732 397 4 , , PUNCT ejpam-6732 397 5 2021 2021 NUM ejpam-6732 397 6 . . PUNCT ejpam-6732 398 1 article article NOUN ejpam-6732 398 2 i i PROPN ejpam-6732 398 3 d d PROPN ejpam-6732 398 4 6615604 6615604 NUM ejpam-6732 398 5 . . PUNCT ejpam-6732 399 1 [ [ X ejpam-6732 399 2 8 8 NUM ejpam-6732 399 3 ] ] PUNCT ejpam-6732 399 4 a. a. NOUN ejpam-6732 399 5 ajaib ajaib PROPN ejpam-6732 399 6 and and CCONJ ejpam-6732 399 7 a. a. NOUN ejpam-6732 399 8 hussain hussain PROPN ejpam-6732 399 9 . . PUNCT ejpam-6732 400 1 weighted weight VERB ejpam-6732 400 2 cbmo cbmo NOUN ejpam-6732 400 3 estimates estimate NOUN ejpam-6732 400 4 for for ADP ejpam-6732 400 5 commutators commutator NOUN ejpam-6732 400 6 of of ADP ejpam-6732 400 7 matrix matrix NOUN ejpam-6732 400 8 hausdorff hausdorff NOUN ejpam-6732 400 9 operator operator NOUN ejpam-6732 400 10 on on ADP ejpam-6732 400 11 the the DET ejpam-6732 400 12 heisenberg heisenberg PROPN ejpam-6732 400 13 group group NOUN ejpam-6732 400 14 . . PUNCT ejpam-6732 401 1 open open ADJ ejpam-6732 401 2 mathematics mathematic NOUN ejpam-6732 401 3 , , PUNCT ejpam-6732 401 4 18:496–511 18:496–511 PROPN ejpam-6732 401 5 , , PUNCT ejpam-6732 401 6 2020 2020 NUM ejpam-6732 401 7 . . PUNCT ejpam-6732 402 1 [ [ X ejpam-6732 402 2 9 9 NUM ejpam-6732 402 3 ] ] PUNCT ejpam-6732 402 4 m. m. NOUN ejpam-6732 402 5 sultan sultan PROPN ejpam-6732 402 6 , , PUNCT ejpam-6732 402 7 b. b. PROPN ejpam-6732 402 8 sultan sultan PROPN ejpam-6732 402 9 , , PUNCT ejpam-6732 402 10 and and CCONJ ejpam-6732 402 11 a. a. NOUN ejpam-6732 402 12 hussain hussain PROPN ejpam-6732 402 13 . . PUNCT ejpam-6732 403 1 grand grand PROPN ejpam-6732 403 2 herz herz PROPN ejpam-6732 403 3 – – PUNCT ejpam-6732 403 4 morrey morrey PROPN ejpam-6732 403 5 spaces space VERB ejpam-6732 403 6 with with ADP ejpam-6732 403 7 variable variable ADJ ejpam-6732 403 8 exponent exponent NOUN ejpam-6732 403 9 . . PUNCT ejpam-6732 404 1 mathematical mathematical ADJ ejpam-6732 404 2 notes note NOUN ejpam-6732 404 3 , , PUNCT ejpam-6732 404 4 114(5):957–977 114(5):957–977 NUM ejpam-6732 404 5 , , PUNCT ejpam-6732 404 6 2023 2023 NUM ejpam-6732 404 7 . . PUNCT ejpam-6732 405 1 [ [ X ejpam-6732 405 2 10 10 NUM ejpam-6732 405 3 ] ] PUNCT ejpam-6732 405 4 a. a. NOUN ejpam-6732 405 5 hussain hussain PROPN ejpam-6732 405 6 and and CCONJ ejpam-6732 405 7 g. g. PROPN ejpam-6732 405 8 gao gao PROPN ejpam-6732 405 9 . . PUNCT ejpam-6732 406 1 multilinear multilinear PROPN ejpam-6732 406 2 singular singular PROPN ejpam-6732 406 3 integrals integral NOUN ejpam-6732 406 4 and and CCONJ ejpam-6732 406 5 commutators commutator NOUN ejpam-6732 406 6 on on ADP ejpam-6732 406 7 herz herz ADJ ejpam-6732 406 8 space space NOUN ejpam-6732 406 9 with with ADP ejpam-6732 406 10 variable variable ADJ ejpam-6732 406 11 exponent exponent NOUN ejpam-6732 406 12 . . PUNCT ejpam-6732 407 1 isrn isrn PROPN ejpam-6732 407 2 mathematical mathematical ADJ ejpam-6732 407 3 analysis analysis NOUN ejpam-6732 407 4 , , PUNCT ejpam-6732 407 5 2014:1–10 2014:1–10 NUM ejpam-6732 407 6 , , PUNCT ejpam-6732 407 7 2014 2014 NUM ejpam-6732 407 8 . . PUNCT ejpam-6732 408 1 [ [ X ejpam-6732 408 2 11 11 NUM ejpam-6732 408 3 ] ] PUNCT ejpam-6732 408 4 a. a. NOUN ejpam-6732 408 5 hussain hussain PROPN ejpam-6732 408 6 , , PUNCT ejpam-6732 408 7 i. i. PROPN ejpam-6732 408 8 khan khan PROPN ejpam-6732 408 9 , , PUNCT ejpam-6732 408 10 and and CCONJ ejpam-6732 408 11 a. a. PROPN ejpam-6732 408 12 mohamed mohamed PROPN ejpam-6732 408 13 . . PUNCT ejpam-6732 409 1 variable variable ADJ ejpam-6732 409 2 herz herz PROPN ejpam-6732 409 3 – – PUNCT ejpam-6732 409 4 morrey morrey PROPN ejpam-6732 409 5 estimates estimate NOUN ejpam-6732 409 6 for for ADP ejpam-6732 409 7 rough rough ADJ ejpam-6732 409 8 fractional fractional ADJ ejpam-6732 409 9 hausdorff hausdorff NOUN ejpam-6732 409 10 operator operator NOUN ejpam-6732 409 11 . . PUNCT ejpam-6732 410 1 journal journal PROPN ejpam-6732 410 2 of of ADP ejpam-6732 410 3 inequalities inequality NOUN ejpam-6732 410 4 and and CCONJ ejpam-6732 410 5 applications application NOUN ejpam-6732 410 6 , , PUNCT ejpam-6732 410 7 2024:33 2024:33 NUM ejpam-6732 410 8 , , PUNCT ejpam-6732 410 9 2024 2024 NUM ejpam-6732 410 10 . . PUNCT ejpam-6732 411 1 [ [ X ejpam-6732 411 2 12 12 NUM ejpam-6732 411 3 ] ] X ejpam-6732 411 4 j. j. PROPN ejpam-6732 411 5 younas younas PROPN ejpam-6732 411 6 , , PUNCT ejpam-6732 411 7 a. a. NOUN ejpam-6732 411 8 hussain hussain PROPN ejpam-6732 411 9 , , PUNCT ejpam-6732 411 10 h. h. PROPN ejpam-6732 411 11 alhazmi alhazmi PROPN ejpam-6732 411 12 , , PUNCT ejpam-6732 411 13 a. a. PROPN ejpam-6732 411 14 f. f. PROPN ejpam-6732 411 15 aljohani aljohani PROPN ejpam-6732 411 16 , , PUNCT ejpam-6732 411 17 and and CCONJ ejpam-6732 411 18 i. i. PROPN ejpam-6732 411 19 khan khan PROPN ejpam-6732 411 20 . . PUNCT ejpam-6732 412 1 bmo bmo PROPN ejpam-6732 412 2 estimates estimate NOUN ejpam-6732 412 3 for for ADP ejpam-6732 412 4 commutators commutator NOUN ejpam-6732 412 5 of of ADP ejpam-6732 412 6 the the DET ejpam-6732 412 7 rough rough ADJ ejpam-6732 412 8 fractional fractional ADJ ejpam-6732 412 9 hausdorff hausdorff NOUN ejpam-6732 412 10 operator operator NOUN ejpam-6732 412 11 on on ADP ejpam-6732 412 12 grand grand ADJ ejpam-6732 412 13 - - PUNCT ejpam-6732 412 14 variable variable ADJ ejpam-6732 412 15 - - PUNCT ejpam-6732 412 16 herz herz ADJ ejpam-6732 412 17 – – PUNCT ejpam-6732 412 18 morrey morrey PROPN ejpam-6732 412 19 spaces space VERB ejpam-6732 412 20 . . PUNCT ejpam-6732 413 1 aims aim VERB ejpam-6732 413 2 mathematics mathematic NOUN ejpam-6732 413 3 , , PUNCT ejpam-6732 413 4 9(9):23434–23448 9(9):23434–23448 NUM ejpam-6732 413 5 , , PUNCT ejpam-6732 413 6 2024 2024 NUM ejpam-6732 413 7 . . PUNCT ejpam-6732 414 1 [ [ X ejpam-6732 414 2 13 13 NUM ejpam-6732 414 3 ] ] PUNCT ejpam-6732 414 4 m. m. NOUN ejpam-6732 414 5 sultan sultan PROPN ejpam-6732 414 6 and and CCONJ ejpam-6732 414 7 b. b. PROPN ejpam-6732 414 8 sultan sultan PROPN ejpam-6732 414 9 . . PUNCT ejpam-6732 415 1 a a DET ejpam-6732 415 2 note note NOUN ejpam-6732 415 3 on on ADP ejpam-6732 415 4 the the DET ejpam-6732 415 5 boundedness boundedness NOUN ejpam-6732 415 6 of of ADP ejpam-6732 415 7 marcinkiewicz marcinkiewicz ADJ ejpam-6732 415 8 integral integral ADJ ejpam-6732 415 9 operator operator NOUN ejpam-6732 415 10 on on ADP ejpam-6732 415 11 continual continual ADJ ejpam-6732 415 12 herz herz PROPN ejpam-6732 415 13 – – PUNCT ejpam-6732 415 14 morrey morrey PROPN ejpam-6732 415 15 spaces space VERB ejpam-6732 415 16 . . PUNCT ejpam-6732 416 1 filomat filomat PROPN ejpam-6732 416 2 , , PUNCT ejpam-6732 416 3 39(6):2017–2027 39(6):2017–2027 PROPN ejpam-6732 416 4 , , PUNCT ejpam-6732 416 5 2025 2025 NUM ejpam-6732 416 6 . . PUNCT ejpam-6732 417 1 [ [ X ejpam-6732 417 2 14 14 NUM ejpam-6732 417 3 ] ] PUNCT ejpam-6732 417 4 b. b. PROPN ejpam-6732 417 5 sultan sultan PROPN ejpam-6732 417 6 , , PUNCT ejpam-6732 417 7 f. f. PROPN ejpam-6732 417 8 azmi azmi PROPN ejpam-6732 417 9 , , PUNCT ejpam-6732 417 10 m. m. NOUN ejpam-6732 417 11 sultan sultan PROPN ejpam-6732 417 12 , , PUNCT ejpam-6732 417 13 m. m. NOUN ejpam-6732 417 14 mehmood mehmood PROPN ejpam-6732 417 15 , , PUNCT ejpam-6732 417 16 and and CCONJ ejpam-6732 417 17 n. n. PROPN ejpam-6732 417 18 mlaiki mlaiki PROPN ejpam-6732 417 19 . . PUNCT ejpam-6732 418 1 boundedness boundedness PROPN ejpam-6732 418 2 of of ADP ejpam-6732 418 3 riesz riesz PROPN ejpam-6732 418 4 potential potential ADJ ejpam-6732 418 5 operator operator NOUN ejpam-6732 418 6 on on ADP ejpam-6732 418 7 grand grand ADJ ejpam-6732 418 8 herz herz PROPN ejpam-6732 418 9 – – PUNCT ejpam-6732 418 10 morrey morrey PROPN ejpam-6732 418 11 spaces space NOUN ejpam-6732 418 12 . . PUNCT ejpam-6732 419 1 axioms axiom NOUN ejpam-6732 419 2 , , PUNCT ejpam-6732 419 3 11(11):583 11(11):583 NUM ejpam-6732 419 4 , , PUNCT ejpam-6732 419 5 2022 2022 NUM ejpam-6732 419 6 . . PUNCT ejpam-6732 420 1 [ [ X ejpam-6732 420 2 15 15 NUM ejpam-6732 420 3 ] ] X ejpam-6732 420 4 b. b. PROPN ejpam-6732 420 5 sultan sultan PROPN ejpam-6732 420 6 , , PUNCT ejpam-6732 420 7 m. m. NOUN ejpam-6732 420 8 sultan sultan PROPN ejpam-6732 420 9 , , PUNCT ejpam-6732 420 10 m. m. PROPN ejpam-6732 420 11 mehmood mehmood PROPN ejpam-6732 420 12 , , PUNCT ejpam-6732 420 13 f. f. PROPN ejpam-6732 420 14 azmi azmi PROPN ejpam-6732 420 15 , , PUNCT ejpam-6732 420 16 m. m. NOUN ejpam-6732 420 17 a. a. NOUN ejpam-6732 420 18 alghafli alghafli PROPN ejpam-6732 420 19 , , PUNCT ejpam-6732 420 20 and and CCONJ ejpam-6732 420 21 n. n. PROPN ejpam-6732 420 22 mlaiki mlaiki PROPN ejpam-6732 420 23 . . PUNCT ejpam-6732 421 1 boundedness boundedness PROPN ejpam-6732 421 2 of of ADP ejpam-6732 421 3 fractional fractional ADJ ejpam-6732 421 4 integrals integral NOUN ejpam-6732 421 5 on on ADP ejpam-6732 421 6 grand grand ADJ ejpam-6732 421 7 weighted weight VERB ejpam-6732 421 8 herz herz PROPN ejpam-6732 421 9 spaces space NOUN ejpam-6732 421 10 with with ADP ejpam-6732 421 11 variable variable ADJ ejpam-6732 421 12 exponent exponent NOUN ejpam-6732 421 13 . . PUNCT ejpam-6732 422 1 aims aim VERB ejpam-6732 422 2 mathematics mathematic NOUN ejpam-6732 422 3 , , PUNCT ejpam-6732 422 4 8(1):752–764 8(1):752–764 NUM ejpam-6732 422 5 , , PUNCT ejpam-6732 422 6 2023 2023 NUM ejpam-6732 422 7 . . PUNCT ejpam-6732 423 1 [ [ X ejpam-6732 423 2 16 16 NUM ejpam-6732 423 3 ] ] PUNCT ejpam-6732 423 4 b. b. PROPN ejpam-6732 423 5 sultan sultan PROPN ejpam-6732 423 6 , , PUNCT ejpam-6732 423 7 f. f. PROPN ejpam-6732 423 8 azmi azmi PROPN ejpam-6732 423 9 , , PUNCT ejpam-6732 423 10 m. m. NOUN ejpam-6732 423 11 sultan sultan PROPN ejpam-6732 423 12 , , PUNCT ejpam-6732 423 13 t. t. PROPN ejpam-6732 423 14 mahmood mahmood PROPN ejpam-6732 423 15 , , PUNCT ejpam-6732 423 16 n. n. PROPN ejpam-6732 423 17 mlaiki mlaiki PROPN ejpam-6732 423 18 , , PUNCT ejpam-6732 423 19 and and CCONJ ejpam-6732 423 20 n. n. NOUN ejpam-6732 423 21 souayah souayah NOUN ejpam-6732 423 22 . . PUNCT ejpam-6732 424 1 boundedness boundedness NOUN ejpam-6732 424 2 of of ADP ejpam-6732 424 3 fractional fractional ADJ ejpam-6732 424 4 integrals integral NOUN ejpam-6732 424 5 on on ADP ejpam-6732 424 6 grand grand ADJ ejpam-6732 424 7 weighted weight VERB ejpam-6732 424 8 herz herz PROPN ejpam-6732 424 9 – – PUNCT ejpam-6732 424 10 morrey morrey PROPN ejpam-6732 424 11 spaces space VERB ejpam-6732 424 12 with with ADP ejpam-6732 424 13 variable variable ADJ ejpam-6732 424 14 exponent exponent NOUN ejpam-6732 424 15 . . PUNCT ejpam-6732 425 1 fractal fractal PROPN ejpam-6732 425 2 and and CCONJ ejpam-6732 425 3 fractional fractional ADJ ejpam-6732 425 4 , , PUNCT ejpam-6732 425 5 6(11):660–670 6(11):660–670 NUM ejpam-6732 425 6 , , PUNCT ejpam-6732 425 7 2022 2022 NUM ejpam-6732 425 8 . . PUNCT ejpam-6732 426 1 [ [ X ejpam-6732 426 2 17 17 NUM ejpam-6732 426 3 ] ] PUNCT ejpam-6732 426 4 b. b. PROPN ejpam-6732 426 5 sultan sultan PROPN ejpam-6732 426 6 , , PUNCT ejpam-6732 426 7 m. m. NOUN ejpam-6732 426 8 sultan sultan PROPN ejpam-6732 426 9 , , PUNCT ejpam-6732 426 10 q. q. PROPN ejpam-6732 426 11 q. q. PROPN ejpam-6732 426 12 zhang zhang PROPN ejpam-6732 426 13 , , PUNCT ejpam-6732 426 14 and and CCONJ ejpam-6732 426 15 n. n. PROPN ejpam-6732 426 16 mlaiki mlaiki PROPN ejpam-6732 426 17 . . PUNCT ejpam-6732 427 1 boundedness boundedness PROPN ejpam-6732 427 2 of of ADP ejpam-6732 427 3 hardy hardy ADJ ejpam-6732 427 4 operators operator NOUN ejpam-6732 427 5 on on ADP ejpam-6732 427 6 grand grand ADJ ejpam-6732 427 7 variable variable NOUN ejpam-6732 427 8 weighted weight VERB ejpam-6732 427 9 herz herz PROPN ejpam-6732 427 10 spaces space NOUN ejpam-6732 427 11 . . PUNCT ejpam-6732 428 1 aims aim VERB ejpam-6732 428 2 mathematics mathematic NOUN ejpam-6732 428 3 , , PUNCT ejpam-6732 428 4 8(10):24515–24527 8(10):24515–24527 NUM ejpam-6732 428 5 , , PUNCT ejpam-6732 428 6 2023 2023 NUM ejpam-6732 428 7 . . PUNCT ejpam-6732 429 1 [ [ X ejpam-6732 429 2 18 18 NUM ejpam-6732 429 3 ] ] PUNCT ejpam-6732 429 4 m. m. NOUN ejpam-6732 429 5 sultan sultan PROPN ejpam-6732 429 6 , , PUNCT ejpam-6732 429 7 b. b. PROPN ejpam-6732 429 8 sultan sultan PROPN ejpam-6732 429 9 , , PUNCT ejpam-6732 429 10 a. a. PROPN ejpam-6732 429 11 khan khan PROPN ejpam-6732 429 12 , , PUNCT ejpam-6732 429 13 and and CCONJ ejpam-6732 429 14 t. t. PROPN ejpam-6732 429 15 abdeljawad abdeljawad NOUN ejpam-6732 429 16 . . PUNCT ejpam-6732 430 1 boundedness boundedness NOUN ejpam-6732 430 2 of of ADP ejpam-6732 430 3 marcinkiewicz marcinkiewicz ADJ ejpam-6732 430 4 integral integral ADJ ejpam-6732 430 5 operator operator NOUN ejpam-6732 430 6 of of ADP ejpam-6732 430 7 variable variable ADJ ejpam-6732 430 8 order order NOUN ejpam-6732 430 9 in in ADP ejpam-6732 430 10 grand grand ADJ ejpam-6732 430 11 herz herz PROPN ejpam-6732 430 12 – – PUNCT ejpam-6732 430 13 morrey morrey PROPN ejpam-6732 430 14 spaces space NOUN ejpam-6732 430 15 . . PUNCT ejpam-6732 431 1 aims aim VERB ejpam-6732 431 2 mathematics mathematic NOUN ejpam-6732 431 3 , , PUNCT ejpam-6732 431 4 8(9):22338–22353 8(9):22338–22353 PROPN ejpam-6732 431 5 , , PUNCT ejpam-6732 431 6 2023 2023 NUM ejpam-6732 431 7 . . PUNCT ejpam-6732 432 1 [ [ X ejpam-6732 432 2 19 19 NUM ejpam-6732 432 3 ] ] PUNCT ejpam-6732 432 4 b. b. PROPN ejpam-6732 432 5 sultan sultan PROPN ejpam-6732 432 6 and and CCONJ ejpam-6732 432 7 m. m. PROPN ejpam-6732 432 8 sultan sultan PROPN ejpam-6732 432 9 . . PUNCT ejpam-6732 433 1 boundedness boundedness NOUN ejpam-6732 433 2 of of ADP ejpam-6732 433 3 higher high ADJ ejpam-6732 433 4 order order NOUN ejpam-6732 433 5 commutators commutator NOUN ejpam-6732 433 6 of of ADP ejpam-6732 433 7 hardy hardy ADJ ejpam-6732 433 8 operators operator NOUN ejpam-6732 433 9 on on ADP ejpam-6732 433 10 grand grand ADJ ejpam-6732 433 11 herz herz PROPN ejpam-6732 433 12 – – PUNCT ejpam-6732 433 13 morrey morrey PROPN ejpam-6732 433 14 spaces space NOUN ejpam-6732 433 15 . . PUNCT ejpam-6732 434 1 bulletin bulletin PROPN ejpam-6732 434 2 des des PROPN ejpam-6732 434 3 sciences sciences PROPN ejpam-6732 434 4 mathématiques mathématiques PROPN ejpam-6732 434 5 , , PUNCT ejpam-6732 434 6 190:103390 190:103390 NUM ejpam-6732 434 7 , , PUNCT ejpam-6732 434 8 b. b. PROPN ejpam-6732 434 9 sultan sultan PROPN ejpam-6732 434 10 et et PROPN ejpam-6732 434 11 al al PROPN ejpam-6732 434 12 . . PUNCT ejpam-6732 434 13 / / SYM ejpam-6732 434 14 eur eur PROPN ejpam-6732 434 15 . . PUNCT ejpam-6732 435 1 j. j. PROPN ejpam-6732 435 2 pure pure PROPN ejpam-6732 435 3 appl appl PROPN ejpam-6732 435 4 . . PROPN ejpam-6732 435 5 math math PROPN ejpam-6732 435 6 , , PUNCT ejpam-6732 435 7 18 18 NUM ejpam-6732 435 8 ( ( PUNCT ejpam-6732 435 9 4 4 NUM ejpam-6732 435 10 ) ) PUNCT ejpam-6732 435 11 ( ( PUNCT ejpam-6732 435 12 2025 2025 NUM ejpam-6732 435 13 ) ) PUNCT ejpam-6732 435 14 , , PUNCT ejpam-6732 435 15 6732 6732 NUM ejpam-6732 435 16 19 19 NUM ejpam-6732 435 17 of of ADP ejpam-6732 435 18 20 20 NUM ejpam-6732 435 19 2024 2024 NUM ejpam-6732 435 20 . . PUNCT ejpam-6732 436 1 [ [ X ejpam-6732 436 2 20 20 NUM ejpam-6732 436 3 ] ] PUNCT ejpam-6732 436 4 m. m. NOUN ejpam-6732 436 5 sultan sultan PROPN ejpam-6732 436 6 and and CCONJ ejpam-6732 436 7 b. b. PROPN ejpam-6732 436 8 sultan sultan PROPN ejpam-6732 436 9 . . PUNCT ejpam-6732 437 1 boundedness boundedness PROPN ejpam-6732 437 2 of of ADP ejpam-6732 437 3 sublinear sublinear NOUN ejpam-6732 437 4 operators operator NOUN ejpam-6732 437 5 on on ADP ejpam-6732 437 6 grand grand ADJ ejpam-6732 437 7 central central ADJ ejpam-6732 437 8 orlicz orlicz NOUN ejpam-6732 437 9 – – PUNCT ejpam-6732 437 10 morrey morrey PROPN ejpam-6732 437 11 spaces space VERB ejpam-6732 437 12 . . PUNCT ejpam-6732 438 1 bulletin bulletin PROPN ejpam-6732 438 2 des des PROPN ejpam-6732 438 3 sciences sciences PROPN ejpam-6732 438 4 mathématiques mathématiques PROPN ejpam-6732 438 5 , , PUNCT ejpam-6732 438 6 205:103704 205:103704 NUM ejpam-6732 438 7 , , PUNCT ejpam-6732 438 8 2025 2025 NUM ejpam-6732 438 9 . . PUNCT ejpam-6732 439 1 [ [ X ejpam-6732 439 2 21 21 NUM ejpam-6732 439 3 ] ] PUNCT ejpam-6732 439 4 m. m. NOUN ejpam-6732 439 5 sultan sultan PROPN ejpam-6732 439 6 and and CCONJ ejpam-6732 439 7 b. b. PROPN ejpam-6732 439 8 sultan sultan PROPN ejpam-6732 439 9 . . PUNCT ejpam-6732 440 1 λ λ ADJ ejpam-6732 440 2 - - ADJ ejpam-6732 440 3 central central ADJ ejpam-6732 440 4 musielak musielak NOUN ejpam-6732 440 5 – – PUNCT ejpam-6732 440 6 orlicz orlicz NUM ejpam-6732 440 7 – – PUNCT ejpam-6732 440 8 morrey morrey NOUN ejpam-6732 440 9 spaces space NOUN ejpam-6732 440 10 . . PUNCT ejpam-6732 441 1 arabian arabian ADJ ejpam-6732 441 2 journal journal PROPN ejpam-6732 441 3 of of ADP ejpam-6732 441 4 mathematics mathematic NOUN ejpam-6732 441 5 , , PUNCT ejpam-6732 441 6 14:357–363 14:357–363 NUM ejpam-6732 441 7 , , PUNCT ejpam-6732 441 8 2025 2025 NUM ejpam-6732 441 9 . . PUNCT ejpam-6732 442 1 [ [ X ejpam-6732 442 2 22 22 NUM ejpam-6732 442 3 ] ] PUNCT ejpam-6732 442 4 b. b. PROPN ejpam-6732 442 5 sultan sultan PROPN ejpam-6732 442 6 , , PUNCT ejpam-6732 442 7 m. m. NOUN ejpam-6732 442 8 sultan sultan PROPN ejpam-6732 442 9 , , PUNCT ejpam-6732 442 10 and and CCONJ ejpam-6732 442 11 a. a. NOUN ejpam-6732 442 12 hussain hussain PROPN ejpam-6732 442 13 . . PUNCT ejpam-6732 443 1 boundedness boundedness NOUN ejpam-6732 443 2 of of ADP ejpam-6732 443 3 the the DET ejpam-6732 443 4 bochner bochner NOUN ejpam-6732 443 5 – – PUNCT ejpam-6732 443 6 riesz riesz NOUN ejpam-6732 443 7 operators operator NOUN ejpam-6732 443 8 on on ADP ejpam-6732 443 9 the the DET ejpam-6732 443 10 weighted weight VERB ejpam-6732 443 11 herz herz PROPN ejpam-6732 443 12 – – PUNCT ejpam-6732 443 13 morrey morrey PROPN ejpam-6732 443 14 type type NOUN ejpam-6732 443 15 hardy hardy ADJ ejpam-6732 443 16 spaces space NOUN ejpam-6732 443 17 . . PUNCT ejpam-6732 444 1 complex complex ADJ ejpam-6732 444 2 analysis analysis NOUN ejpam-6732 444 3 and and CCONJ ejpam-6732 444 4 operator operator NOUN ejpam-6732 444 5 theory theory NOUN ejpam-6732 444 6 , , PUNCT ejpam-6732 444 7 19:49 19:49 NUM ejpam-6732 444 8 , , PUNCT ejpam-6732 444 9 2025 2025 NUM ejpam-6732 444 10 . . PUNCT ejpam-6732 445 1 [ [ X ejpam-6732 445 2 23 23 NUM ejpam-6732 445 3 ] ] PUNCT ejpam-6732 445 4 b. b. PROPN ejpam-6732 445 5 sultan sultan PROPN ejpam-6732 445 6 , , PUNCT ejpam-6732 445 7 a. a. NOUN ejpam-6732 445 8 hussain hussain PROPN ejpam-6732 445 9 , , PUNCT ejpam-6732 445 10 and and CCONJ ejpam-6732 445 11 m. m. NOUN ejpam-6732 445 12 sultan sultan PROPN ejpam-6732 445 13 . . PUNCT ejpam-6732 446 1 characterization characterization NOUN ejpam-6732 446 2 of of ADP ejpam-6732 446 3 generalized generalized ADJ ejpam-6732 446 4 campanato campanato NOUN ejpam-6732 446 5 spaces space NOUN ejpam-6732 446 6 with with ADP ejpam-6732 446 7 variable variable ADJ ejpam-6732 446 8 exponents exponent NOUN ejpam-6732 446 9 via via ADP ejpam-6732 446 10 fractional fractional ADJ ejpam-6732 446 11 integrals integral NOUN ejpam-6732 446 12 . . PUNCT ejpam-6732 447 1 journal journal NOUN ejpam-6732 447 2 of of ADP ejpam-6732 447 3 pseudo pseudo NOUN ejpam-6732 447 4 - - ADJ ejpam-6732 447 5 differential differential ADJ ejpam-6732 447 6 operators operator NOUN ejpam-6732 447 7 and and CCONJ ejpam-6732 447 8 applications application NOUN ejpam-6732 447 9 , , PUNCT ejpam-6732 447 10 16:22 16:22 NUM ejpam-6732 447 11 , , PUNCT ejpam-6732 447 12 2025 2025 NUM ejpam-6732 447 13 . . PUNCT ejpam-6732 448 1 [ [ X ejpam-6732 448 2 24 24 NUM ejpam-6732 448 3 ] ] PUNCT ejpam-6732 448 4 b. b. PROPN ejpam-6732 448 5 sultan sultan PROPN ejpam-6732 448 6 , , PUNCT ejpam-6732 448 7 m. m. NOUN ejpam-6732 448 8 sultan sultan PROPN ejpam-6732 448 9 , , PUNCT ejpam-6732 448 10 a. a. PROPN ejpam-6732 448 11 khan khan PROPN ejpam-6732 448 12 , , PUNCT ejpam-6732 448 13 and and CCONJ ejpam-6732 448 14 t. t. PROPN ejpam-6732 448 15 abdeljawad abdeljawad NOUN ejpam-6732 448 16 . . PUNCT ejpam-6732 449 1 boundedness boundedness NOUN ejpam-6732 449 2 of of ADP ejpam-6732 449 3 commutators commutator NOUN ejpam-6732 449 4 of of ADP ejpam-6732 449 5 variable variable ADJ ejpam-6732 449 6 marcinkiewicz marcinkiewicz ADJ ejpam-6732 449 7 fractional fractional ADJ ejpam-6732 449 8 integral integral ADJ ejpam-6732 449 9 operator operator NOUN ejpam-6732 449 10 in in ADP ejpam-6732 449 11 grand grand ADJ ejpam-6732 449 12 variable variable ADJ ejpam-6732 449 13 herz herz PROPN ejpam-6732 449 14 spaces space NOUN ejpam-6732 449 15 . . PUNCT ejpam-6732 450 1 journal journal PROPN ejpam-6732 450 2 of of ADP ejpam-6732 450 3 inequalities inequality NOUN ejpam-6732 450 4 and and CCONJ ejpam-6732 450 5 applications application NOUN ejpam-6732 450 6 , , PUNCT ejpam-6732 450 7 2024:93 2024:93 NUM ejpam-6732 450 8 , , PUNCT ejpam-6732 450 9 2024 2024 NUM ejpam-6732 450 10 . . PUNCT ejpam-6732 451 1 [ [ X ejpam-6732 451 2 25 25 NUM ejpam-6732 451 3 ] ] PUNCT ejpam-6732 451 4 b. b. PROPN ejpam-6732 451 5 sultan sultan PROPN ejpam-6732 451 6 and and CCONJ ejpam-6732 451 7 m. m. PROPN ejpam-6732 451 8 sultan sultan PROPN ejpam-6732 451 9 . . PUNCT ejpam-6732 452 1 sobolev sobolev NOUN ejpam-6732 452 2 - - PUNCT ejpam-6732 452 3 type type NOUN ejpam-6732 452 4 theorem theorem NOUN ejpam-6732 452 5 for for ADP ejpam-6732 452 6 commutators commutator NOUN ejpam-6732 452 7 of of ADP ejpam-6732 452 8 hardy hardy ADJ ejpam-6732 452 9 operators operator NOUN ejpam-6732 452 10 in in ADP ejpam-6732 452 11 grand grand ADJ ejpam-6732 452 12 herz herz PROPN ejpam-6732 452 13 spaces space NOUN ejpam-6732 452 14 . . PUNCT ejpam-6732 453 1 ukrainian ukrainian ADJ ejpam-6732 453 2 mathematical mathematical ADJ ejpam-6732 453 3 journal journal NOUN ejpam-6732 453 4 , , PUNCT ejpam-6732 453 5 76:1196–1213 76:1196–1213 NUM ejpam-6732 453 6 , , PUNCT ejpam-6732 453 7 2024 2024 NUM ejpam-6732 453 8 . . PUNCT ejpam-6732 454 1 [ [ X ejpam-6732 454 2 26 26 NUM ejpam-6732 454 3 ] ] PUNCT ejpam-6732 454 4 m. m. NOUN ejpam-6732 454 5 sultan sultan PROPN ejpam-6732 454 6 , , PUNCT ejpam-6732 454 7 b. b. PROPN ejpam-6732 454 8 sultan sultan PROPN ejpam-6732 454 9 , , PUNCT ejpam-6732 454 10 and and CCONJ ejpam-6732 454 11 r. r. PROPN ejpam-6732 454 12 e. e. PROPN ejpam-6732 454 13 castillo castillo PROPN ejpam-6732 454 14 . . PUNCT ejpam-6732 455 1 weighted weight VERB ejpam-6732 455 2 composition composition NOUN ejpam-6732 455 3 operator operator NOUN ejpam-6732 455 4 on on ADP ejpam-6732 455 5 gamma gamma NOUN ejpam-6732 455 6 spaces space NOUN ejpam-6732 455 7 with with ADP ejpam-6732 455 8 variable variable ADJ ejpam-6732 455 9 exponent exponent NOUN ejpam-6732 455 10 . . PUNCT ejpam-6732 456 1 journal journal PROPN ejpam-6732 456 2 of of ADP ejpam-6732 456 3 pseudo pseudo NOUN ejpam-6732 456 4 - - ADJ ejpam-6732 456 5 differential differential ADJ ejpam-6732 456 6 operators operator NOUN ejpam-6732 456 7 and and CCONJ ejpam-6732 456 8 applications application NOUN ejpam-6732 456 9 , , PUNCT ejpam-6732 456 10 15:46 15:46 NUM ejpam-6732 456 11 , , PUNCT ejpam-6732 456 12 2024 2024 NUM ejpam-6732 456 13 . . PUNCT ejpam-6732 457 1 [ [ X ejpam-6732 457 2 27 27 NUM ejpam-6732 457 3 ] ] PUNCT ejpam-6732 457 4 m. m. NOUN ejpam-6732 457 5 sultan sultan PROPN ejpam-6732 457 6 and and CCONJ ejpam-6732 457 7 b. b. PROPN ejpam-6732 457 8 sultan sultan PROPN ejpam-6732 457 9 . . PUNCT ejpam-6732 458 1 a a DET ejpam-6732 458 2 note note NOUN ejpam-6732 458 3 on on ADP ejpam-6732 458 4 the the DET ejpam-6732 458 5 boundedness boundedness NOUN ejpam-6732 458 6 of of ADP ejpam-6732 458 7 higher high ADJ ejpam-6732 458 8 order order NOUN ejpam-6732 458 9 commutators commutator NOUN ejpam-6732 458 10 on on ADP ejpam-6732 458 11 fractional fractional ADJ ejpam-6732 458 12 integrals integral NOUN ejpam-6732 458 13 in in ADP ejpam-6732 458 14 grand grand ADJ ejpam-6732 458 15 variable variable ADJ ejpam-6732 458 16 herz herz PROPN ejpam-6732 458 17 – – PUNCT ejpam-6732 458 18 morrey morrey PROPN ejpam-6732 458 19 spaces space VERB ejpam-6732 458 20 . . PUNCT ejpam-6732 459 1 kragujevac kragujevac PROPN ejpam-6732 459 2 journal journal PROPN ejpam-6732 459 3 of of ADP ejpam-6732 459 4 mathematics mathematic NOUN ejpam-6732 459 5 , , PUNCT ejpam-6732 459 6 50(7):1063–1080 50(7):1063–1080 NUM ejpam-6732 459 7 , , PUNCT ejpam-6732 459 8 2026 2026 NUM ejpam-6732 459 9 . . PUNCT ejpam-6732 460 1 [ [ X ejpam-6732 460 2 28 28 NUM ejpam-6732 460 3 ] ] X ejpam-6732 460 4 j. j. PROPN ejpam-6732 460 5 xu xu PROPN ejpam-6732 460 6 and and CCONJ ejpam-6732 460 7 x. x. PROPN ejpam-6732 460 8 yang yang PROPN ejpam-6732 460 9 . . PUNCT ejpam-6732 461 1 herz herz PROPN ejpam-6732 461 2 – – PUNCT ejpam-6732 461 3 morrey morrey ADJ ejpam-6732 461 4 – – PUNCT ejpam-6732 461 5 hardy hardy ADJ ejpam-6732 461 6 spaces space NOUN ejpam-6732 461 7 with with ADP ejpam-6732 461 8 variable variable ADJ ejpam-6732 461 9 exponents exponent NOUN ejpam-6732 461 10 and and CCONJ ejpam-6732 461 11 their their PRON ejpam-6732 461 12 applications application NOUN ejpam-6732 461 13 . . PUNCT ejpam-6732 462 1 journal journal NOUN ejpam-6732 462 2 of of ADP ejpam-6732 462 3 function function NOUN ejpam-6732 462 4 spaces space NOUN ejpam-6732 462 5 , , PUNCT ejpam-6732 462 6 2015:19 2015:19 NUM ejpam-6732 462 7 , , PUNCT ejpam-6732 462 8 2015 2015 NUM ejpam-6732 462 9 . . PUNCT ejpam-6732 463 1 [ [ X ejpam-6732 463 2 29 29 NUM ejpam-6732 463 3 ] ] PUNCT ejpam-6732 463 4 t. t. PROPN ejpam-6732 463 5 anh anh PROPN ejpam-6732 463 6 , , PUNCT ejpam-6732 463 7 j. j. PROPN ejpam-6732 463 8 cao cao PROPN ejpam-6732 463 9 , , PUNCT ejpam-6732 463 10 l. l. PROPN ejpam-6732 463 11 d. d. PROPN ejpam-6732 463 12 ky ky PROPN ejpam-6732 463 13 , , PUNCT ejpam-6732 463 14 d. d. PROPN ejpam-6732 463 15 yang yang PROPN ejpam-6732 463 16 , , PUNCT ejpam-6732 463 17 and and CCONJ ejpam-6732 463 18 s. s. PROPN ejpam-6732 463 19 yang yang PROPN ejpam-6732 463 20 . . PROPN ejpam-6732 463 21 weighted weight VERB ejpam-6732 463 22 hardy hardy ADJ ejpam-6732 463 23 spaces space NOUN ejpam-6732 463 24 associated associate VERB ejpam-6732 463 25 with with ADP ejpam-6732 463 26 operators operator NOUN ejpam-6732 463 27 satisfying satisfy VERB ejpam-6732 463 28 reinforced reinforce VERB ejpam-6732 463 29 off off ADP ejpam-6732 463 30 - - PUNCT ejpam-6732 463 31 diagonal diagonal ADJ ejpam-6732 463 32 estimates estimate NOUN ejpam-6732 463 33 . . PUNCT ejpam-6732 464 1 taiwanese taiwanese ADJ ejpam-6732 464 2 journal journal NOUN ejpam-6732 464 3 of of ADP ejpam-6732 464 4 mathematics mathematic NOUN ejpam-6732 464 5 , , PUNCT ejpam-6732 464 6 17(4):1127–1166 17(4):1127–1166 NUM ejpam-6732 464 7 , , PUNCT ejpam-6732 464 8 2013 2013 NUM ejpam-6732 464 9 . . PUNCT ejpam-6732 465 1 [ [ X ejpam-6732 465 2 30 30 NUM ejpam-6732 465 3 ] ] X ejpam-6732 465 4 x. x. NOUN ejpam-6732 465 5 fu fu PROPN ejpam-6732 465 6 , , PUNCT ejpam-6732 465 7 h. h. PROPN ejpam-6732 465 8 lin lin PROPN ejpam-6732 465 9 , , PUNCT ejpam-6732 465 10 d. d. PROPN ejpam-6732 465 11 yang yang PROPN ejpam-6732 465 12 , , PUNCT ejpam-6732 465 13 and and CCONJ ejpam-6732 465 14 d. d. PROPN ejpam-6732 465 15 yang yang PROPN ejpam-6732 465 16 . . PUNCT ejpam-6732 466 1 hardy hardy ADJ ejpam-6732 466 2 spaces space NOUN ejpam-6732 466 3 hp hp VERB ejpam-6732 466 4 over over ADP ejpam-6732 466 5 non non ADJ ejpam-6732 466 6 - - ADJ ejpam-6732 466 7 homogeneous homogeneous ADJ ejpam-6732 466 8 metric metric ADJ ejpam-6732 466 9 measure measure NOUN ejpam-6732 466 10 spaces space NOUN ejpam-6732 466 11 and and CCONJ ejpam-6732 466 12 their their PRON ejpam-6732 466 13 applications application NOUN ejpam-6732 466 14 . . PUNCT ejpam-6732 467 1 science science PROPN ejpam-6732 467 2 china china PROPN ejpam-6732 467 3 mathematics mathematics PROPN ejpam-6732 467 4 , , PUNCT ejpam-6732 467 5 58(2):309–388 58(2):309–388 NUM ejpam-6732 467 6 , , PUNCT ejpam-6732 467 7 2015 2015 NUM ejpam-6732 467 8 . . PUNCT ejpam-6732 468 1 [ [ X ejpam-6732 468 2 31 31 NUM ejpam-6732 468 3 ] ] PUNCT ejpam-6732 468 4 r. r. PROPN ejpam-6732 468 5 gong gong PROPN ejpam-6732 468 6 , , PUNCT ejpam-6732 468 7 j. j. PROPN ejpam-6732 468 8 li li PROPN ejpam-6732 468 9 , , PUNCT ejpam-6732 468 10 and and CCONJ ejpam-6732 468 11 l. l. PROPN ejpam-6732 468 12 yan yan PROPN ejpam-6732 468 13 . . PUNCT ejpam-6732 469 1 a a DET ejpam-6732 469 2 local local ADJ ejpam-6732 469 3 version version NOUN ejpam-6732 469 4 of of ADP ejpam-6732 469 5 hardy hardy ADJ ejpam-6732 469 6 spaces space NOUN ejpam-6732 469 7 associated associate VERB ejpam-6732 469 8 with with ADP ejpam-6732 469 9 operators operator NOUN ejpam-6732 469 10 on on ADP ejpam-6732 469 11 metric metric ADJ ejpam-6732 469 12 spaces space NOUN ejpam-6732 469 13 . . PUNCT ejpam-6732 470 1 science science PROPN ejpam-6732 470 2 china china PROPN ejpam-6732 470 3 mathematics mathematics PROPN ejpam-6732 470 4 , , PUNCT ejpam-6732 470 5 56(2):315–330 56(2):315–330 PROPN ejpam-6732 470 6 , , PUNCT ejpam-6732 470 7 2013 2013 NUM ejpam-6732 470 8 . . PUNCT ejpam-6732 471 1 [ [ X ejpam-6732 471 2 32 32 NUM ejpam-6732 471 3 ] ] PUNCT ejpam-6732 471 4 s. s. PROPN ejpam-6732 471 5 samko samko PROPN ejpam-6732 471 6 . . PUNCT ejpam-6732 472 1 variable variable ADJ ejpam-6732 472 2 exponent exponent PROPN ejpam-6732 472 3 herz herz PROPN ejpam-6732 472 4 spaces space VERB ejpam-6732 472 5 . . PUNCT ejpam-6732 473 1 mediterranean mediterranean PROPN ejpam-6732 473 2 journal journal PROPN ejpam-6732 473 3 of of ADP ejpam-6732 473 4 mathematics mathematic NOUN ejpam-6732 473 5 , , PUNCT ejpam-6732 473 6 10(4):2007–2025 10(4):2007–2025 NUM ejpam-6732 473 7 , , PUNCT ejpam-6732 473 8 2013 2013 NUM ejpam-6732 473 9 . . PUNCT ejpam-6732 474 1 [ [ X ejpam-6732 474 2 33 33 NUM ejpam-6732 474 3 ] ] PUNCT ejpam-6732 474 4 m. m. NOUN ejpam-6732 474 5 izuki izuki PROPN ejpam-6732 474 6 . . PUNCT ejpam-6732 475 1 boundedness boundedness PROPN ejpam-6732 475 2 of of ADP ejpam-6732 475 3 commutators commutator NOUN ejpam-6732 475 4 on on ADP ejpam-6732 475 5 herz herz PROPN ejpam-6732 475 6 spaces space NOUN ejpam-6732 475 7 with with ADP ejpam-6732 475 8 variable variable ADJ ejpam-6732 475 9 exponent exponent NOUN ejpam-6732 475 10 . . PUNCT ejpam-6732 476 1 rendiconti rendiconti PROPN ejpam-6732 476 2 del del PROPN ejpam-6732 476 3 circolo circolo PROPN ejpam-6732 476 4 matematico matematico NOUN ejpam-6732 476 5 di di NOUN ejpam-6732 476 6 palermo palermo NOUN ejpam-6732 476 7 , , PUNCT ejpam-6732 476 8 59:199–213 59:199–213 PROPN ejpam-6732 476 9 , , PUNCT ejpam-6732 476 10 2010 2010 NUM ejpam-6732 476 11 . . PUNCT ejpam-6732 477 1 [ [ X ejpam-6732 477 2 34 34 NUM ejpam-6732 477 3 ] ] X ejpam-6732 477 4 d. d. PROPN ejpam-6732 477 5 cruz cruz PROPN ejpam-6732 477 6 - - PUNCT ejpam-6732 477 7 uribe uribe PROPN ejpam-6732 477 8 and and CCONJ ejpam-6732 477 9 a. a. NOUN ejpam-6732 477 10 fiorenza fiorenza PROPN ejpam-6732 477 11 . . PUNCT ejpam-6732 478 1 variable variable ADJ ejpam-6732 478 2 lebesgue lebesgue PROPN ejpam-6732 478 3 spaces space VERB ejpam-6732 478 4 : : PUNCT ejpam-6732 478 5 foundations foundation NOUN ejpam-6732 478 6 and and CCONJ ejpam-6732 478 7 harmonic harmonic ADJ ejpam-6732 478 8 analysis analysis NOUN ejpam-6732 478 9 . . PUNCT ejpam-6732 479 1 applied apply VERB ejpam-6732 479 2 and and CCONJ ejpam-6732 479 3 numerical numerical ADJ ejpam-6732 479 4 harmonic harmonic ADJ ejpam-6732 479 5 analysis analysis NOUN ejpam-6732 479 6 . . PUNCT ejpam-6732 480 1 birkhäuser birkhäuser NOUN ejpam-6732 480 2 , , PUNCT ejpam-6732 480 3 heidelberg heidelberg NOUN ejpam-6732 480 4 , , PUNCT ejpam-6732 480 5 2013 2013 NUM ejpam-6732 480 6 . . PUNCT ejpam-6732 481 1 [ [ X ejpam-6732 481 2 35 35 NUM ejpam-6732 481 3 ] ] X ejpam-6732 481 4 b. b. PROPN ejpam-6732 481 5 muckenhoupt muckenhoupt PROPN ejpam-6732 481 6 and and CCONJ ejpam-6732 481 7 r. r. PROPN ejpam-6732 481 8 l. l. PROPN ejpam-6732 481 9 wheeden wheeden PROPN ejpam-6732 481 10 . . PUNCT ejpam-6732 482 1 weighted weight VERB ejpam-6732 482 2 norm norm NOUN ejpam-6732 482 3 inequalities inequality NOUN ejpam-6732 482 4 for for ADP ejpam-6732 482 5 singular singular ADJ ejpam-6732 482 6 and and CCONJ ejpam-6732 482 7 fractional fractional ADJ ejpam-6732 482 8 integrals integral NOUN ejpam-6732 482 9 . . PUNCT ejpam-6732 483 1 transactions transaction NOUN ejpam-6732 483 2 of of ADP ejpam-6732 483 3 the the DET ejpam-6732 483 4 american american PROPN ejpam-6732 483 5 mathematical mathematical PROPN ejpam-6732 483 6 society society NOUN ejpam-6732 483 7 , , PUNCT ejpam-6732 483 8 161:249–258 161:249–258 NUM ejpam-6732 483 9 , , PUNCT ejpam-6732 483 10 1971 1971 NUM ejpam-6732 483 11 . . PUNCT ejpam-6732 484 1 [ [ X ejpam-6732 484 2 36 36 NUM ejpam-6732 484 3 ] ] X ejpam-6732 484 4 j. j. PROPN ejpam-6732 484 5 l. l. PROPN ejpam-6732 484 6 wu wu PROPN ejpam-6732 484 7 andw andw PROPN ejpam-6732 484 8 . . PUNCT ejpam-6732 485 1 j. j. PROPN ejpam-6732 485 2 zhao zhao PROPN ejpam-6732 485 3 . . PUNCT ejpam-6732 486 1 boundedness boundedness PROPN ejpam-6732 486 2 for for ADP ejpam-6732 486 3 fractional fractional ADJ ejpam-6732 486 4 hardy hardy ADJ ejpam-6732 486 5 - - PUNCT ejpam-6732 486 6 type type NOUN ejpam-6732 486 7 operator operator NOUN ejpam-6732 486 8 on on ADP ejpam-6732 486 9 variableb variableb NOUN ejpam-6732 486 10 . . PUNCT ejpam-6732 487 1 sultan sultan PROPN ejpam-6732 487 2 et et PROPN ejpam-6732 487 3 al al PROPN ejpam-6732 487 4 . . PUNCT ejpam-6732 487 5 / / SYM ejpam-6732 487 6 eur eur PROPN ejpam-6732 487 7 . . PUNCT ejpam-6732 488 1 j. j. PROPN ejpam-6732 488 2 pure pure PROPN ejpam-6732 488 3 appl appl PROPN ejpam-6732 488 4 . . PROPN ejpam-6732 488 5 math math PROPN ejpam-6732 488 6 , , PUNCT ejpam-6732 488 7 18 18 NUM ejpam-6732 488 8 ( ( PUNCT ejpam-6732 488 9 4 4 NUM ejpam-6732 488 10 ) ) PUNCT ejpam-6732 488 11 ( ( PUNCT ejpam-6732 488 12 2025 2025 NUM ejpam-6732 488 13 ) ) PUNCT ejpam-6732 488 14 , , PUNCT ejpam-6732 488 15 6732 6732 NUM ejpam-6732 488 16 20 20 NUM ejpam-6732 488 17 of of ADP ejpam-6732 488 18 20 20 NUM ejpam-6732 488 19 exponent exponent ADJ ejpam-6732 488 20 herz herz PROPN ejpam-6732 488 21 – – PUNCT ejpam-6732 488 22 morrey morrey PROPN ejpam-6732 488 23 spaces space NOUN ejpam-6732 488 24 . . PUNCT ejpam-6732 489 1 kyoto kyoto PROPN ejpam-6732 489 2 journal journal PROPN ejpam-6732 489 3 of of ADP ejpam-6732 489 4 mathematics mathematic NOUN ejpam-6732 489 5 , , PUNCT ejpam-6732 489 6 56(4):831–845 56(4):831–845 NUM ejpam-6732 489 7 , , PUNCT ejpam-6732 489 8 2016 2016 NUM ejpam-6732 489 9 . . PUNCT ejpam-6732 490 1 [ [ X ejpam-6732 490 2 37 37 NUM ejpam-6732 490 3 ] ] X ejpam-6732 490 4 v. v. ADP ejpam-6732 490 5 kokilashvili kokilashvili PROPN ejpam-6732 490 6 and and CCONJ ejpam-6732 490 7 s. s. PROPN ejpam-6732 490 8 samko samko PROPN ejpam-6732 490 9 . . PUNCT ejpam-6732 491 1 on on ADP ejpam-6732 491 2 sobolev sobolev PROPN ejpam-6732 491 3 theorem theorem NOUN ejpam-6732 491 4 for for ADP ejpam-6732 491 5 riesz riesz NOUN ejpam-6732 491 6 - - PUNCT ejpam-6732 491 7 type type NOUN ejpam-6732 491 8 potentials potential NOUN ejpam-6732 491 9 in in ADP ejpam-6732 491 10 the the DET ejpam-6732 491 11 lebesgue lebesgue NOUN ejpam-6732 491 12 spaces space NOUN ejpam-6732 491 13 with with ADP ejpam-6732 491 14 variable variable ADJ ejpam-6732 491 15 exponent exponent NOUN ejpam-6732 491 16 . . PUNCT ejpam-6732 492 1 zeitschrift zeitschrift NOUN ejpam-6732 492 2 für für PROPN ejpam-6732 492 3 analysis analysis NOUN ejpam-6732 492 4 und und VERB ejpam-6732 492 5 ihre ihre ADJ ejpam-6732 492 6 anwendungen anwendungen NOUN ejpam-6732 492 7 , , PUNCT ejpam-6732 492 8 22:899–910 22:899–910 PROPN ejpam-6732 492 9 , , PUNCT ejpam-6732 492 10 2003 2003 NUM ejpam-6732 492 11 . . PUNCT ejpam-6732 493 1 introduction introduction NOUN ejpam-6732 493 2 and and CCONJ ejpam-6732 493 3 preliminaries preliminary NOUN ejpam-6732 493 4 the the DET ejpam-6732 493 5 atomic atomic ADJ ejpam-6732 493 6 characterization characterization NOUN