Open AccessA Kind of Estimate of Difference Norms in Anisotropic Weighted Sobolev-Lorentz Spaces
Author(s) -
Jiecheng Chen,
Hongliang Li
Publication year - 2009
Publication title -
journal of inequalities and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 50
eISSN - 1029-242X
pISSN - 1025-5834
DOI - 10.1155/2009/161405
Subject(s) - lorentz transformation , sobolev space , pure mathematics , mathematics , work (physics) , type (biology) , mathematical economics , physics , geology , classical mechanics , paleontology , thermodynamics
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
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