Chapter of Book
Improving bounds for singular operators via sharp reverse Hölder inequality for A∞
Author/s | Ortiz Caraballo, Carmen María
Pérez Moreno, Carlos Rela, Ezequiel |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2013 |
Deposit Date | 2016-10-11 |
Published in |
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ISBN/ISSN | 9783034805155 9783034805162 |
Abstract | 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 ... 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∞. |
Project ID. | MTM2009-08934
FQM-4745 |
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