Sharp reverse Hölder property for A∞ weights on spaces of homogeneous type
In this article we present a new proof of a sharp Reverse Hölder Inequality for A∞ weights. Then we derive two applications: a precise open property of Muckenhoupt classes and, as a consequence of this last result, we obtain a simple proof of a sharp weighted bound for the Hardy-Littlewood maximal f...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/45011 |
| Acceso en línea: | http://hdl.handle.net/11441/45011 https://doi.org/10.1016/j.jfa.2012.09.013 |
| Access Level: | acceso abierto |
| Palabra clave: | Space of homogeneous type Muckenhoupt weights Reverse Hölder Maximal functions |
| Sumario: | In this article we present a new proof of a sharp Reverse Hölder Inequality for A∞ weights. Then we derive two applications: a precise open property of Muckenhoupt classes and, as a consequence of this last result, we obtain a simple proof of a sharp weighted bound for the Hardy-Littlewood maximal function involving A∞ constants: kMkLp(w) ≤ c 1 p − 1 [w]Ap [σ]A∞ 1/p , where 1 < p < ∞, σ = w 1 1−p and c is a dimensional constant. Our approach allows us to extend the result to the context of spaces of homogeneous type and prove a weak Reverse H¨older Inequality which is still sufficient to prove the open property for Ap classes and the Lp boundedness of the maximal function. In this latter case, the constant c appearing in the norm inequality for the maximal function depends only on the doubling constant of the measure µ and the geometric constant κ of the quasimetric. |
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