A note on one sided extrapolation of compactness and applications

TL;DR

This paper extends compactness extrapolation results to one-sided operators, leading to new compactness results for one-sided singular integrals, commutators, and H"ormander operators, with some findings being novel even in classical contexts.

Contribution

It provides one-sided counterparts of existing compactness extrapolation results and introduces new compactness results for certain operators, including some novel in classical analysis.

Findings

Compactness results for one-sided singular integrals

Compactness of commutators of one-sided fractional integrals

New results on $L^{r}$-H"ormander operators in classical setting

Abstract

In this paper one sided counterparts of compactness extrapolation results of Hyt\"onen and Lappas are provided. As a consequence of those results, compactness results for one sided singular integrals, commutators of one sided fractional integrals and a certain class of $L^{r}$-H\"ormander operators are provided. The results for commutators of $L^{r}$-H\"ormander operators seem new even in the classical setting.