Interior estimates in Morrey spaces for solutions of elliptic equations and weighted boundedness for commutators of singular integral operators

被引：48

作者：

Liu, LZ ^{[1
]}

机构：

[1] Changsha Univ Sci & Technol, Coll Math & Comp, Changsha 410077, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2005年 / 25卷 / 01期

关键词：

nondivergence elliptic equation; generalized Morrey space; commutator of singular integral operator; A(p) weight;

D O I：

10.1016/S0252-9602(17)30264-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that, for the nondivergence elliptic equations Sigma(i,j=1)(n) a(ij)u(xixj) = f, if f belongs to the generalized Morrey spaces L-p,(phi)(omega), then u(xixj) is an element of L-p,L-phi(omega), where u is the W-2,W-p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on L-p,L-phi(omega).

引用

页码：89 / 94

页数：6

共 10 条

[1] Chiarenza F., 1991, RIC MAT, V40, P149
[2] Chiarenza F., 1987, Rend Mat Appl (7), V7, P273
[3] EXTENSIONS OF HARDY SPACES AND THEIR USE IN ANALYSIS
COIFMAN, RR
WEISS, G
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 83 (04) : 569 - 645
[4] ANOTHER CHARACTERIZATION OF BMO
COIFMAN, RR
ROCHBERG, R
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 79 (02) : 249 - 254
[5] DeFrancia J.L.R., 1985, WEIGHTED NORM INEQUA
[6] DIFAZIO G, 1991, B UNIONE MAT ITAL, V5A, P323
[7] INTERIOR ESTIMATES IN MORREY SPACES FOR STRONG SOLUTIONS TO NONDIVERGENCE FORM EQUATIONS WITH DISCONTINUOUS COEFFICIENTS
DIFAZIO, G
RAGUSA, MA
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1993, 112 (02) : 241 - 256
[8] Gilbert, 1983, ELLIPTIC PARTIAL DIF
[9] LIU LZ, 1994, NE MATH J, V10, P365
[10] LIU LZ, 2000, KYUNGPOOK MATH J, V40, P333

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