id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ijassa-292	Liu, Chun-Tai; Deng, Guo-Tai	Characterization of $L_c^p$ -solutions for the Dilation Equations on $R^2$	2011	10	.pdf	application/pdf	3550	230	86	For 1 ≤ p <∞, equation(7) has a (nonzero)Lpc−solution if and only if either c01 + c11 = 2 and 1 4 (|c00 + c10|p + |2− (c00 + c10)|p) < 1 or c00 + c10 = 2 and c02 + c12 = 2. Proof Note that M1 = ( c00 0 c02 c01 ) ,M2 = ( c01 c00 0 c02 ) ,M3 = ( c10 0 c12 c11 ) ,M4 = ( c11 c10 0 c12 ) , and M1 +M2 +M3 +M4 = ( c00 + c10 + c01 + c11 c00 + c10 c02 + c12 c01 + c11 + c02 + c12 ) . = 1 4 ( M1 +M2 +M3 +M4 )∫ T Fk(x) dx = 1 4 (M1 +M2 +M3 +M4)v = v. Theorem 2.7.	cache/ijassa-292.pdf	txt/ijassa-292.txt