Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces
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 wi...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2003 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:2009 |
| Acesso em linha: | https://ddd.uab.cat/record/2009 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_47103_04 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Weyl fractional integral Weigths Weighted Lebesgue and Lipschitz spaces Weighted BMO |
| Resumo: | 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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