This note is devoted to the study of Hyt{o}nens 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.
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