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

Abstract

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

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}

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

CLC Number:

42B20

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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.

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