Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 835938, 17 pages
doi:10.1155/2008/835938
Research Article

Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels

Xiangxing Tao,1 Xiao Yu,1,2 and Songyan Zhang1

1Department of Mathematics, Faculty of Science, Ningbo University, Ningbo, Zhejiang Province 315211, China
2Department of Mathematics, Faculty of Science, Zhejiang University, Hangzhou, Zhejiang Province 315211, China

Received 3 August 2008; Accepted 20 October 2008

Academic Editor: Nikolaos Papageorgiou

Copyright © 2008 Xiangxing Tao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The existence and boundedness on Sobolev spaces and Hardy-Sobolev spaces for the hypersingular Marcinkiewicz integrals with variable kernels are derived.