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Estimates of difference norms for functions in anisotropic Sobolev spaces
Author(s) -
Kolyada V. I.,
Pérez F. J.
Publication year - 2004
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310152
Subject(s) - mathematics , sobolev space , lorentz transformation , interpolation space , lorentz space , pure mathematics , cover (algebra) , type (biology) , besov space , anisotropy , birnbaum–orlicz space , mathematical analysis , functional analysis , geology , mechanical engineering , biochemistry , chemistry , physics , classical mechanics , gene , paleontology , quantum mechanics , engineering
Abstract We investigate the spaces of functions on ℝ n for which the generalized partial derivatives D r kk f exist and belong to different Lorentz spaces L p k ,s k. For the functions in these spaces, the sharp estimates of the Besov type norms are found. The methods used in the paper are based on estimates of non‐increasing rearrangements. These methods enable us to cover also the case when some of the p k 's are equal to 1. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)