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Vietnam Journal of Mathematics 35:3(2007) 267-273

 Weighted Inequalities for Commutators of Singular Integral Operators and Interior Estimates in

Morrey Spaces for Solutions of Elliptic Equations

Zhou Xiaosha

Abstract.  In this paper, the weighted inequalities for the commutators of some singular integral operators on the Morrey spaces L^p,φ(ω) are obtained. As an application, it is proved that, for the nondivergence elliptic equations , if f belongs to L^p,φ(ω), then u_xixj L^p,φ(ω), where u is the W^2,p-solution of the equations.

2000 Mathematics Subject Classification: 42B20, 42B25, 35A.

Keywords: Commutator of singular integral operator; Morrey space; Nondivergence elliptic equation; A_p weight.

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