2020/12/31 by Tuomas Hytönen, Stefanos Lappas
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Applied mathematics #Bilinear interpolation #Compact space #Discrete mathematics #Extrapolation #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Pure mathematics #Statistics #math.CA #math.FA #msc:42B20 #msc:42B35 #msc:46B70 #msc:47B38 #msc:47H60
paper · pdf · doi:10.1016/j.indag.2021.09.007
published as Indag. Math. 33 (2), (2022), 397-420 · v3: final version, incorporated referee comments, to appear in Indagationes Mathematicae, 27 pages
arxiv created 2021/09/22 · openalex publication_date 2021/09/29 · openalex created_date 2021/10/11 · arxiv updated 2022/02/23 · openalex updated_date 2026/08/05
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 Calderón–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 Fréchet–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.