Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces
In this paper we introduce the one-sided weighted spaces Lw -(β), -1 < β < 1. The purpose of this definition is to obtain an extension of the Weyl fractional integral operator I α + from Lw p. into a suitable weighted space. Under certain condition on the weight w, we have that L w -(β...
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2003
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paper:paper_02141493_v47_n1_p71_Ombrosi2023-06-08T15:20:52Z Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces Ombrosi, Sheldy Javier De Rosa, Liliana Noemí Weighted BMO Weighted Lebesgue and Lipschitz spaces Weigths Weyl fractional integral In this paper we introduce the one-sided weighted spaces Lw -(β), -1 < β < 1. The purpose of this definition is to obtain an extension of the Weyl fractional integral operator I α + from Lw p. into a suitable weighted space. Under certain condition on the weight w, we have that L w -(β) coincides with the dual of the Hardy space H- 1 (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 Lw - (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 Iα + from Lw p into L w - (β), -1 < β < 1, and its extension to a bounded operator from Lw - (0) into Lw -(α). Fil:Ombrosi, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:De Rosa, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2003 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v47_n1_p71_Ombrosi http://hdl.handle.net/20.500.12110/paper_02141493_v47_n1_p71_Ombrosi |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Weighted BMO Weighted Lebesgue and Lipschitz spaces Weigths Weyl fractional integral |
| spellingShingle |
Weighted BMO Weighted Lebesgue and Lipschitz spaces Weigths Weyl fractional integral Ombrosi, Sheldy Javier De Rosa, Liliana Noemí Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces |
| topic_facet |
Weighted BMO Weighted Lebesgue and Lipschitz spaces Weigths Weyl fractional integral |
| description |
In this paper we introduce the one-sided weighted spaces Lw -(β), -1 < β < 1. The purpose of this definition is to obtain an extension of the Weyl fractional integral operator I α + from Lw p. into a suitable weighted space. Under certain condition on the weight w, we have that L w -(β) coincides with the dual of the Hardy space H- 1 (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 Lw - (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 Iα + from Lw p into L w - (β), -1 < β < 1, and its extension to a bounded operator from Lw - (0) into Lw -(α). |
| author |
Ombrosi, Sheldy Javier De Rosa, Liliana Noemí |
| author_facet |
Ombrosi, Sheldy Javier De Rosa, Liliana Noemí |
| author_sort |
Ombrosi, Sheldy Javier |
| title |
Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces |
| title_short |
Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces |
| title_full |
Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces |
| title_fullStr |
Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces |
| title_full_unstemmed |
Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces |
| title_sort |
boundedness of the weyl fractional integral on one-sided weighted lebesgue and lipschitz spaces |
| publishDate |
2003 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v47_n1_p71_Ombrosi http://hdl.handle.net/20.500.12110/paper_02141493_v47_n1_p71_Ombrosi |
| work_keys_str_mv |
AT ombrosisheldyjavier boundednessoftheweylfractionalintegralononesidedweightedlebesgueandlipschitzspaces AT derosaliliananoemi boundednessoftheweylfractionalintegralononesidedweightedlebesgueandlipschitzspaces |
| _version_ |
1768544683776016384 |