A note on one-sided extrapolation of compactness and applications

In this paper one-sided counterparts of compactness extrapolation results of Hytönen and Lappas (2021) are provided. As a consequence, compactness results for one-sided singular integrals, commutators of one-sided fractional integrals and a certain class of $L^{r}$-Hörmander operators are given. The results for commutators of $L^{r}$-Hörmander operators seem new even in the classical setting.