Entropy Bumps and Another Sufficient Condition for the Two--Weight Boundedness of Sparse Operators
Rob Rahm, Scott Spencer
TL;DR
This paper presents a simplified proof and introduces a new sufficient condition for the two-weight boundedness of sparse operators, advancing understanding of their boundedness criteria.
Contribution
It provides an efficient proof of existing results and proposes a novel sufficient condition for sparse operator boundedness.
Findings
Simplified proof of Treil-Volberg and Lacey-Spencer results
Introduction of a new sufficient condition for two-weight boundedness
Use of Hytönen's formula to achieve results
Abstract
In this short note, we give a very efficient proof of a recent result of Treil-Volberg and Lacey--Spencer giving sufficient conditions for the two-weight boundedness of a sparse operator. We also give a new sufficient condition for the two-weight boundedness of a sparse operator. We make critical use of a formula of Hyt\"onen
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