Sharp weighted estimates involving one supremum

TL;DR

This paper establishes sharp weighted estimates involving a supremum, answering an open question and extending results to rough homogeneous singular integral operators.

Contribution

It provides a positive resolution to an open problem and extends sharp weighted estimates to a broader class of operators.

Findings

Confirmed sharp weighted estimates involving one supremum.

Extended results to rough homogeneous singular integral operators.

Answered an open question by Lerner and Moen.

Abstract

In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen \cite{LM}. We also extend the result to rough homogeneous singular integral operators.