Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 161405, 22 pages
doi:10.1155/2009/161405
Research Article

A Kind of Estimate of Difference Norms in Anisotropic Weighted Sobolev-Lorentz Spaces

Jiecheng Chen1 and Hongliang Li1,2

1Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2Department of Mathematics, Zhejiang Education Institute, Hangzhou 310012, China

Received 27 April 2009; Accepted 2 July 2009

Academic Editor: Shusen Ding

Copyright © 2009 Jiecheng Chen and Hongliang Li. 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

We investigate the functions spaces on ℝn for which the generalized partial derivatives Dkrkf exist and belong to different Lorentz spaces Λpk,sk(w), where pk>1 and w is nonincreasing and satisfies some special conditions. For the functions in these weighted Sobolev-Lorentz spaces, the estimates of the Besov type norms are found. The methods used in the paper are based on some estimates of nonincreasing rearrangements and the application of Bp, Bp,∞ weights.