A note on extrapolation of compactness

TL;DR

This paper investigates the extrapolation of compactness in weighted Lebesgue spaces, providing criteria for compactness of linear operators and applications to various integral operators.

Contribution

It introduces two new criteria for compactness in the two-weight setting and applies them to establish compactness of several important operators.

Findings

Established criteria for compactness in two-weight spaces.

Proved two-weight compactness of commutators of Calderón--Zygmund operators.

Extended results to fractional and bilinear Calderón--Zygmund operators.

Abstract

This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain two-weight compactness of commutators of Calder\'{o}n--Zygmund operators, fractional integrals and bilinear Calder\'{o}n--Zygmund operators.