INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

摘要/Abstract

摘要：

It is proved that, for the nondivergence elliptic equations $\sum_{i,j=1}^n$

$a_{ij}u_{x_ix_j}=f$, if $f$ belongs to the generalized Morrey spaces

$L^{p,\varphi}(\omega)$, then $u_{x_ix_j}\in L^{p, \varphi}(\omega)$, where $u$ is the $W^{2,p}$-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 $L^{p,\varphi}(\omega)$. \noindent\ke{\bf Key words}{\rm Nondivergence elliptic equation, generalized Morrey space, commutator of singular integral operator, $A_p$ weight}

Abstract:

It is proved that, for the nondivergence elliptic equations $\sum_{i,j=1}^n$

$a_{ij}u_{x_ix_j}=f$, if $f$ belongs to the generalized Morrey spaces

$L^{p,\varphi}(\omega)$, then $u_{x_ix_j}\in L^{p, \varphi}(\omega)$, where $u$ is the $W^{2,p}$-solution of the equations. In order to obtain this, the author first establish

Key words: Nondivergence elliptic equation;generalized Morrey space, commutator of
singular integral operator;Ap weight

中图分类号:

42B20

刘岚喆. INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS[J]. 数学物理学报(英文版), 2005, 25(1): 89-94.

LIU Lan-Zhe. INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS[J]. Acta mathematica scientia,Series B, 2005, 25(1): 89-94.

[1]	伍火熊. A LIPSCHITZ ESTIMATE FOR MULTILINEAR OSCILLATORY SINGULAR INTEGRALS WITH ROUGH KERNELS[J]. 数学物理学报(英文版), 2005, 25(4): 761-770.
[2]	胡国恩. ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS[J]. 数学物理学报(英文版), 2005, 25(3): 545-554.
[3]	邓东臯,颜立新. COMMUTATORS OF SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS[J]. 数学物理学报(英文版), 2005, 25(1): 137-144.
[4]	陆善镇, 孟岩, 吴强. LIPSCHITZ ESTIMATES FOR MULTILINEAR SINGULAR INTEGRALS, II[J]. 数学物理学报(英文版), 2004, 24(2): 291-300.
[5]	徐罕, 陈杰诚, 应益明. A NOTE ON MARCINKIEWICZ INTEGRALS WITH H1 KERNELS[J]. 数学物理学报(英文版), 2003, 23(1): 133-138.
[6]	刘宗光. BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL INTEGRATION ON HERZ-TYPE SPACES[J]. 数学物理学报(英文版), 2000, 20(4): 461-470.