Upper endpoint estimates and extrapolation for commutators

TL;DR

This paper revisits upper endpoint estimates for commutators, extending existing extrapolation results and providing multilinear versions, using a specialized BMO subspace.

Contribution

It introduces a new BMO subspace for commutators and derives a multilinear upper endpoint extrapolation result, expanding the theoretical framework.

Findings

Established a new upper endpoint estimate for commutators.

Extended the extrapolation result to multilinear commutators.

Provided a theoretical foundation for future research in harmonic analysis.

Abstract

In this note we revisit the upper endpoint estimates for commutators following the line by Harboure, Segovia and Torrea. Relying upon the suitable BMO subspace suited for the commutator that was introduced by Accomazzo, we obtain a counterpart for commutators of the upper endpoint extrapolation result by Harboure, Mac\'ias and Segovia. Multilinear counterparts are provided as well.