id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-1477	Serenbay, Sevilay Kirci; Tanberkan, Hande	Rate of Convergence in Sobolev Space	2012	5	.pdf	application/pdf	1552	79	76	then ‖B1‖Lp(∆a) + ‖B2‖Lp(∆a) + ‖B3‖Lp(a) ¶ a2(‖ fx x‖Lp(∆a) + ‖ f y y‖Lp(∆a) + ‖ fx y‖Lp(∆a) )δn ‖Bn f − f ‖Lp(∆a) ¶ a2‖ f ‖L2 p(∆a) δn. Using the K-functional we get, ‖Bn f − f ‖Lp(∆a) ¶ eM sup g∈L2 p(∆a) [‖ f − g‖Lp(∆a + ‖g‖L2 p(∆a) δn] since, for a sufficiently large n,δn and from (3), Kp( f ;δ) ¶ δn‖ f ‖Lp(∆a ) + 2a1ω2,p( f ;δ(1/2)) eMKp( f ;δ) ¶ eM[δn‖ f ‖Lp(∆a ) + 2a1ω2,p( f ;δ(1/2))] we obtain (4), ‖Bn f − f ‖Lp(∆a) ¶ Mp[‖ f ‖L2 p(∆a) δn +ω2,p( f ;δ(1/2))].	cache/ejpam-1477.pdf	txt/ejpam-1477.txt