Two weighted inequalities for maximal functions related to Cesàro convergence
We characterize the pairs of weights (u, v) for which the maximal operator Mα- f (x) = supR>0 R-1-α ∫x-Rx-2R |f (s)|(x - R - s)α ds, -1 <α < 0, is of weak and restricted weak type (p, p) with respect to u(x) dx and v(x) dx. As a consequence we obtain analogous results for Mαf (x) = supR>...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2003 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/100612 |
| Acesso em linha: | http://hdl.handle.net/11336/100612 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Two weighted inequalities Cesàro convergence https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | We characterize the pairs of weights (u, v) for which the maximal operator Mα- f (x) = supR>0 R-1-α ∫x-Rx-2R |f (s)|(x - R - s)α ds, -1 <α < 0, is of weak and restricted weak type (p, p) with respect to u(x) dx and v(x) dx. As a consequence we obtain analogous results for Mαf (x) = supR>0 R-1-α ∫R<|x-y|<2R |f(y)|(|x - y| -R)α dy. We apply the results to the study of the Cesàro-α convergence of singular integrals. |
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