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 Lʳ-H\"ormander operators are provided. The results for commutators of Lʳ-H\"ormander operators seem new even in the classical setting.
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Martín-Reyes et al. (2024) studied this question.
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