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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)

Data: 2003
Resum: 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).
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Weyl fractional integral ; Weigths ; Weighted Lebesgue and Lipschitz spaces ; Weighted BMO
Publicat a: Publicacions matematiques, V. 47 N. 1 (2003) , p. 71-102, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_47103_04

32 p, 265.7 KB

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