Recent Issues Volume 37 1 2 3 4 Volume 36 1 2 3 4 Volume 35 1 2 3 4 Volume 34 1 2 3 4 Volume 33 1 2 3 4 Past Issues The Journal Cover Aims and Scope Subscription Information Editorial Board Instructions for Author Contact Us Related Links

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 $L^{p,\varphi}(\omega)$ are obtained. As an application, 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 $L^{p,\varphi}(\omega)$, then $u_{x_ix_j}\in L^{p,\varphi}(\omega)$, where $u$ is the $W^{2,p}$-solution of the equations.   2000 Mathematics Subject Classification: 42B20, 42B25, 35A. Keywords: Commutator of singular integral operator; Morrey space; Nondivergence elliptic equation; $A_p$ weight.

Vietnam Academy of Science and Technology & Vietnamese Mathematical Society © Copyright 2009 Vietnam Journal of Mathematics. All rights reserved.