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Sparse domination results for compactness on weighted spaces

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Abstract

By means of appropriate sparse bounds, we deduce compactness on weighted \(L^p(w)\) spaces, \(1<p<\infty\), for all Calderón–Zygmund operators having compact extensions on \(L^2({\mathbb {R}}^n)\). Similar methods lead to new results on boundedness and compactness of Haar multipliers on weighted spaces. In particular, we prove weighted bounds for weights in a class strictly larger than the typical \(A_p\) class.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Washington University in St. Louis, One Brookings Drive, St. Louis, MO, 63130, USA

    Cody B. Stockdale & Brett D. Wick

  2. Department of Mathematics, Temple University, N. Broad St., Philadelphia, PA, 19122, USA

    Paco Villarroya

Authors
  1. Cody B. Stockdale
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  2. Paco Villarroya
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  3. Brett D. Wick
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Correspondence to Cody B. Stockdale.

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Villarroya has been partially supported by Spanish Ministerio de Ciencia, Innovación y Universidades, project Grant PGC2018-095366-B-I00.

B. D. Wick’s research is supported in part by National Science Foundation Grant DMS #1560955 and #1800057, and by Australian Research Council grant DP 190100970.

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Stockdale, C.B., Villarroya, P. & Wick, B.D. Sparse domination results for compactness on weighted spaces. Collect. Math. 73, 535–563 (2022). https://doi.org/10.1007/s13348-021-00333-6

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  • DOI: https://doi.org/10.1007/s13348-021-00333-6

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