A sharpness result for powers of Besov functions. Issue 3 (2004)

• Record Type: Journal Article
• Authors: Bourdaud Bourdaud, Gérard Gérard
• Other Names: Appell Appell Jürgen Jürgen Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2:Issue 3(2004)
• Page Start: 267
• Page End: 277
• Publication Date: 2004
• Subjects: Besov spaces, composition operators.; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2004/823103
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : A recent result of Kateb asserts that f ∈ B p, q s ( ℝ n ) implies | f | μ ∈ B p, q s ( ℝ n ) 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.