Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces
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Autores: Liliana de Rosa, Sheldy J. Ombrosi
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 47, Nº 1, 2003, págs. 71-102
- Idioma: inglés
- DOI: 10.5565/publmat_47103_04
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Resumen
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).
