Extrapolation of compactness on weighted spaces : Bilinear operators

In a previous paper, we obtained several "compact versions" of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue spaces, where these operators are bounded. In this paper, we study the extrapolation of compactness for bilinear operators in terms of bilinear Muckenhoupt weights. As applications, we easily recover and improve earlier results on the weighted compactness of commutators of bilinear Calderon-Zygmund operators, bilinear fractional integrals and bilinear Fourier multipliers. More general versions of these results are recently due to Cao, Olivo and Yabuta (arXiv:2011.13191), whose approach depends on developing weighted versions of the Frechet-Kolmogorov criterion of compactness, whereas we avoid this by relying on "softer" tools, which might have an independent interest in view of further extensions of the method. (C) 2021 TheAuthor(s). Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG).Peer reviewe