A sharpness result for powers of Besov functionsReport as inadecuate




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Journal of Function Spaces and Applications - Volume 2 2004, Issue 3, Pages 267-277

Institut de Mathématiques de Jussieu, Équipe d-Analyse Fonctionnelle, Case 186, 4 place Jussieu, 75252 Paris Cedex 05, France

Received 1 March 2003

Academic Editor: Jürgen Appell

Copyright © 2004 Hindawi Publishing Corporation. 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

A recent result of Kateb asserts that f∈Bp,qsℝn implies |f|μ∈Bp,qsℝn as soon as the following three conditions hold: 1 0≺s≺μ+1-p, 2 f is bounded, 3 μ≻1. By means of counterexamples, we prove that those conditions are optimal.





Author: Gérard Bourdaud

Source: https://www.hindawi.com/



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