Sparse domination results for compactness on weighted spaces

• Stockdale, Cody B. ^[1] ; Wick, Brett D. ^[1] ; Villarroya, Paco ^[2]
  1. [1] Washington University in St. Louis

     Washington University in St. Louis

     Estados Unidos

     
  2. [2] Temple University

     Temple University

     City of Philadelphia, Estados Unidos

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 3, 2022, págs. 535-563
• Idioma: inglés
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• Resumen

  • By means of appropriate sparse bounds, we deduce compactness on weighted L^p(w) spaces, 1p\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.