A note on one sided extrapolation of compactness and applications

In this paper one sided counterparts of compactness extrapolation results of Hytönen 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 $L^r$-Hörmander operators are provided. The results for commutators of $L^r$-Hörmander operators seem new even in the classical setting.