The dual conjecture of Muckenhoupt and Wheeden

• Adam Osękowski ^[1]
  1. [1] University of Warsaw

     University of Warsaw

     Warszawa, Polonia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 6, 2021, págs. 2285-2308
• Idioma: inglés
• DOI: 10.4171/rmi/1264
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let T be a Calderón–Zygmund operator on Rd. We prove the existence of a constant CT,d<∞ such that for any weight w on Rd satisfying Muckenhoupt's condition A1, we have w({x∈Rd:|Tf(x)|>w(x)})≤CT,d[w]A1∫Rdfdx.

    The linear dependence on [w]A1, the A1 characteristic of w, is optimal. The proof exploits the associated dimension-free inequalities for dyadic shifts.