Two-weight inequalities for multilinear commutators in product spaces

TL;DR

This paper develops two-weight estimates for multilinear commutators of singular integrals within product spaces, introducing a novel extrapolation technique to extend results to quasi-Banach spaces.

Contribution

It introduces a new two-weight extrapolation method for multilinear commutators in product spaces, expanding the range of applicable estimates.

Findings

Established two-weight estimates for multilinear commutators.

Developed a new extrapolation technique for quasi-Banach spaces.

Extended the range of estimates to broader function spaces.

Abstract

This note is devoted to establishing two-weight estimates for commutators of singular integrals. We combine multilinearity with product spaces. A new type of two-weight extrapolation result is used to yield the quasi-Banach range of estimates.