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 50 条

[31] Variation operators for singular integrals and their commutators on weighted Morrey spaces and Sobolev spaces
Feng Liu
Peng Cui
[J]. Science China Mathematics, 2022, 65 : 1267 - 1292
[32] Weighted boundedness for multilinear singular integral operators with non-smooth kernels on Morrey spaces
Zhou Xiaosha
Liu Lanzhe
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2010, 104 (01) : 115 - 127
[33] Commutators of singular integral operators on Morrey spaces with some growth functions
Mizuhara, T
[J]. PROCEEDINGS OF THE SECOND ISAAC CONGRESS, VOLS 1 AND 2, 2000, 7 : 65 - 73
[34] VARIATION OPERATORS FOR COMMUTATORS OF ROUGH SINGULAR INTEGRALS ON WEIGHTED MORREY SPACES
Liu, Feng
Fu, Zunwei
Wu, Yan
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2024, 14 (01): : 263 - 282
[35] Singular Integral Equations in Generalized Weighted Morrey Spaces
Persson, Lars-Erik
Samko, Natasha
[J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III, 2010, 1281 : 498 - +
[36] Weighted estimates for singular integral operators and commutators associated with the sections
Tang, Lin
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 333 (02) : 577 - 590
[37] Boundedness of multilinear singular integral operators on the homogeneous Morrey–Herz spaces
Jianglong Wu
[J]. Ukrainian Mathematical Journal, 2009, 61 : 1684 - 1693
[38] ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND SINGULAR INTEGRAL OPERATORS IN GENERALIZED MORREY SPACES
Akbulut, Ali
Guliyev, Vagif
Mustafayev, Rza
[J]. MATHEMATICA BOHEMICA, 2012, 137 (01): : 27 - 43
[39] Some Estimates for Generalized Commutators of Rough Fractional Maximal and Integral Operators on Generalized Weighted Morrey Spaces
Gurbuz, Ferit
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2017, 60 (01): : 131 - 145
[40] Multilinear Singular and Fractional Integral Operators on Weighted Morrey Spaces
Wang, Hua
Yi, Wentan
[J]. JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013,

← 1 2 3 4 5 →