Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
Let b be a BMO function, 0 < α < 1 and I+,k α,b the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator I+,k α,b and for the pairs of weights of the type (w,...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2008 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/84138 |
| Acesso em linha: | http://hdl.handle.net/11336/84138 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Commutators Riemann-Liouville And Weyl Fractional Integrals Weighted Inequalities https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Let b be a BMO function, 0 < α < 1 and I+,k α,b the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator I+,k α,b and for the pairs of weights of the type (w, Mw), where w is any weight and M is a suitable one-sided maximal operator. We also prove that, for A+∞ weights, the operator I +,kα,b is controlled in the Lp (w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide a different way to obtain known results about the operators I +,kα,b. The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral I -,kα,b. |
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