  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.
