Maximal functions and the control of weighted inequalities for the fractional integral operator
We study weak-type (1, 1) weighted inequalities for the fractional integral operator Iα. We show that the fractional maximal operator Mα controls these inequalities when the weight is radially decreasing. However, we exhibit some counterexamples which show that Mα is not appropriate for this control...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42383 |
| Acceso en línea: | http://hdl.handle.net/11441/42383 https://doi.org/10.1512/iumj.2005.54.2714 |
| Access Level: | acceso abierto |
| Palabra clave: | weighted inequalities maximal operator fractional integral |
| Sumario: | We study weak-type (1, 1) weighted inequalities for the fractional integral operator Iα. We show that the fractional maximal operator Mα controls these inequalities when the weight is radially decreasing. However, we exhibit some counterexamples which show that Mα is not appropriate for this control on general weights. We do provide, nevertheless, some positive results related to this problem by considering other suitable maximal functions. |
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