Off-diagonal bloom weighted estimates for bilinear commutators

TL;DR

This paper establishes off-diagonal estimates for bilinear iterated commutators in a two-weight setting, using sparse domination for upper bounds and median methods for lower bounds, with extensions to multilinear cases.

Contribution

It introduces new off-diagonal estimates for bilinear commutators in two-weight scenarios, employing flexible methods that extend to multilinear contexts.

Findings

Established off-diagonal bounds via sparse domination.

Proved lower bounds using median method.

Methods are adaptable to multilinear operators.

Abstract

We prove the off-diagonal estimates of the bilinear iterated commutators in the two-weight setting. The upper bound is established via sparse domination, and the lower bound is proved by the median method. Our methods are so flexible so that it can be easily extended to the multilinear scenario.