Improving bounds for singular operators via sharp reverse Hölder inequality for A∞
In this expository article we collect and discuss some recent results on different consequences of a Sharp Reverse Hölder Inequality for A∞ weights. For two given operators T and S, we study Lp(w) bounds of CoifmanFefferman type: kT fkLp(w) ≤ cn,w,pkSfkLp(w), that can be understood as a way to contr...
| Autores: | , , |
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| Tipo de recurso: | capítulo de libro |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47396 |
| Acceso en línea: | http://hdl.handle.net/11441/47396 https://doi.org/10.1007/978-3-0348-0516-2_17 |
| Access Level: | acceso abierto |
| Palabra clave: | Weighted norm inequalities Reverse Hölder Inequality Maximal operators Singular integrals Calderón-Zygmund theory Commutators |
| Sumario: | In this expository article we collect and discuss some recent results on different consequences of a Sharp Reverse Hölder Inequality for A∞ weights. For two given operators T and S, we study Lp(w) bounds of CoifmanFefferman type: kT fkLp(w) ≤ cn,w,pkSfkLp(w), that can be understood as a way to control T by S. We will focus on a quantitative analysis of the constants involved and show that we can improve classical results regarding the dependence on the weight w in terms of Wilson’s A∞ constant [w]A∞ := sup Q 1 w(Q) Z Q M(wχQ). We will also exhibit recent improvements on the problem of finding sharp constants for weighted norm inequalities involving several singular operators In the same spirit as in T. Hytönen and C. Perez, Sharp weighted bounds involving A∞, we obtain mixed A1-A∞ estimates for the commutator [b, T] and for its higher order analogue Tk b. A common ingredient in the proofs presented here is a recent improvement of the Reverse Hölder Inequality for A∞ weights involving Wilson’s constant from T. Hytönen and C. Perez, Sharp weighted bounds involving A∞. |
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