Off-diagonal compactness extrapolation principles for commutators

Tuomas Oikari

Published 2024-02-07Version 1

We provide new off-diagonal compactness extrapolation principles for commutators of bounded singular integral operators, both of Calder\'on-Zygmund and of rough type. These principles unify the existing theory by streamlining the current state-of-the-art proofs. In particular, we apply them to show that the sufficient conditions for the $L^p$-to-$L^q$ compactness of commutators in the ranges $q>p$ (recently due to Guo et al.) and $q = p$ (classical, due to Uchiyama) and $q<p$ (recently, due to Hyt\"onen et al.) all quickly follow from each other.