Upper endpoint estimates and extrapolation for commutators

Abstract

In this note we revisit the upper endpoint estimates for commutatorsfollowing the line by Harboure, Segovia, and Torrea [Illinois J. Math.41 no. 4 (1997), 676–700]. Relying upon the suitable BMO subspace suitedfor the commutator that was introduced in Accomazzo’s PhD thesis (2020),we obtain a counterpart for commutators of the upper endpoint extrapolationresult by Harboure, Macías and Segovia [Amer. J. Math. 110 no. 3 (1988),383–397]. Multilinear counterparts are provided as well.