The A_p-A_infty inequality for general Calderon--Zygmund operators

TL;DR

This paper establishes a new inequality relating the boundedness of Calderon--Zygmund operators and their maximal truncations in weighted L^p spaces, extending the understanding of operator behavior with respect to Muckenhoupt weights.

Contribution

It introduces an A_p-A_infty inequality for general Calderon--Zygmund operators, providing a novel bound involving A_p and A_infty characteristics.

Findings

Proves a bound for T_# in weighted L^p spaces involving A_p and A_infty constants.

Extends previous inequalities to more general Calderon--Zygmund operators.

Enhances understanding of weighted norm inequalities for singular integral operators.

Abstract

Let T be an arbitrary L^2 bounded Calderon--Zygmund operator, and T_# its maximal truncated version. Then T_# satisfies the following bound for all 1<p<\infty and all weights w\in A_p: \|T_# \|_{L^p(w)} << [w]_{A_p}^{1/p} {[w]_{A_infty}^{1/p'}+[w^{1-p'}]_{A_infty}^{1/p}}.