Two Weight Inequalities for Maximal Truncations of Dyadic Calder\'on-Zygmund Operators

TL;DR

This paper establishes two weight inequalities for maximal truncations of dyadic Calderón-Zygmund operators, providing characterizations and sufficient conditions, including testing conditions, with simplified proofs compared to prior work.

Contribution

It offers new characterizations and sufficient conditions for two weight inequalities in the dyadic Calderón-Zygmund setting, simplifying previous proofs.

Findings

Characterization for one doubling weight case.

Sufficient conditions for the general case.

Simplified proof techniques.

Abstract

We consider L^p two weight inequalities for maximal truncations of dyadic Calderon-Zygmund operators. In the case of one weight being doubling, a characterization is given, and for the general case, sufficient conditions are given, including standard and non-standard testing conditions. The arguments of this paper parallel the authors prior work arXiv:0805.4711, but in this paper are much easier.