Estimates of difference norms for functions in anisotropic Sobolev spaces
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1
Universidad de La Rioja
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2
Karlstad University
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ISSN: 0025-584X
Argitalpen urtea: 2004
Alea: 267
Zenbakia: 267
Orrialdeak: 46-64
Mota: Artikulua
Beste argitalpen batzuk: Mathematische Nachrichten
Laburpena
We investigate the spaces of functions on ℝ n for which the generalized partial derivatives D k rk f exist and belong to different Lorentz spaces L pk, sk. 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.