End-point estimates for iterated commutators of multilinear singular integrals

TL;DR

This paper establishes new endpoint estimates for iterated commutators of multilinear Calderon-Zygmund operators, including weighted and strong type results, advancing understanding of their boundedness in Lebesgue spaces.

Contribution

It provides the first comprehensive endpoint estimates for these commutators, incorporating recent weighted theory and revealing unexpectedly strong bounds for specific multilinear operators.

Findings

Established strong and weak endpoint estimates for iterated commutators

Derived weighted bounds involving vector weights in multilinear Calderon-Zygmund theory

Presented improved estimates for certain multilinear operators

Abstract

Iterated commutators of multilinear Calderon-Zygmund operators and pointwise multiplication with functions in $BMO$ are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted results involving the vectors weights of the multilinear Calderon-Zygmund theory recently introduced in the literature. Some better than expected estimates for certain multilinear operators are presented too.