A Kind of Estimate of Difference Norms in Anisotropic Weighted Sobolev-Lorentz Spaces. (4th August 2009)

• Record Type: Journal Article
• Authors: Chen, Jiecheng; Li, Hongliang
• Other Names: Ding Shusen Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-08-04
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/161405
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : We investigate the functions spaces onℝ n for which the generalized partial derivativesD k r k f exist and belong to different Lorentz spacesΛ p k, s k ( w ), wherep k > 1 andw 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 ofB p, B p, ∞ weights.