Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces
Ombrosi, S. (Universidad de Buenos Aires. Departamento de Matemática)
De Rosa, L. (Universidad de Buenos Aires. Departamento de Matemática)

Date:	2003
Abstract:	In this paper we introduce the one-sided weighted spaces L-w (β), -1 <β< 1. The purpose of this definition is to obtain an extension of the Weyl fractional integral operator I+α from Lp w into a suitable weighted space. Under certain condition on the weight w, we have that L-w (0) coincides with the dual of the Hardy space H1 -(w). We prove for 0 <β< 1, that L- w (β) consists of all functions satisfying a weighted Lipschitz condition. In order to give another characterization of L- w (β), 0 ≤ β < 1, we also prove a one-sided version of John-Nirenberg Inequality. Finally, we obtain necessary and sufficient conditions on the weight w for the boundedness of an extension of I+ α from Lp w into L- w (β), -1 <β< 1, and its extension to a bounded operator from L- w (0) into L- w (α).
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Weyl fractional integral ; Weigths ; Weighted Lebesgue and Lipschitz spaces ; Weighted BMO
Published in:	Publicacions matemàtiques, V. 47 N. 1 (2003) , p. 71-102, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38067
DOI: 10.5565/PUBLMAT_47103_04

32 p, 265.7 KB

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