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- W2953289983 abstract "In this expository article we collect and discuss some recent results on different consequences of a Sharp Reverse Holder Inequality for $A_{infty}$ weights. For two given operators $T$ and $S$, we study $L^p(w)$ bounds of Coifman-Fefferman type. $ |Tf|_{L^p(w)}le c_{n,w,p} |Sf|_{L^p(w)}, $ that can be understood as a way to control $T$ by $S$. We will focus on a emph{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 $A_{infty}$ constant $ [w]_{A_{infty}}:=sup_Qfrac{1}{w(Q)}int_Q M(wchi_Q).$ We will also exhibit recent improvements on the problem of finding sharp constants for weighted norm inequalities involving several singular operators. We obtain mixed $A_{1}$--$A_{infty}$ estimates for the commutator $[b,T]$ and for its higher order analogue $T^k_{b}$. A common ingredient in the proofs presented here is a recent improvement of the Reverse Holder Inequality for $A_{infty}$ weights involving Wilson's constant." @default.
- W2953289983 created "2019-06-27" @default.
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- W2953289983 date "2012-04-07" @default.
- W2953289983 modified "2023-09-27" @default.
- W2953289983 title "Improving bounds for singular operators via Sharp Reverse Holder Inequality for $A_{infty}$" @default.
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