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Muckenhoupt–Wheeden conjectures in higher dimensions

Volume 233 / 2016

Alberto Criado, Fernando Soria Studia Mathematica 233 (2016), 25-45 MSC: Primary 42B20; Secondary 42B25. DOI: 10.4064/sm8357-3-2016 Published online: 2 May 2016

Abstract

In recent work by Reguera and Thiele (2012) and by Reguera and Scurry (2013), two conjectures about joint weighted estimates for Calderón–Zygmund operators and the Hardy–Littlewood maximal function were refuted in the one-dimensional case. One of the key ingredients for these results is the construction of weights for which the value of the Hilbert transform is substantially bigger than that of the maximal function. In this work, we show that a similar construction is possible for classical Calderón–Zygmund operators in higher dimensions. This allows us to fully disprove the conjectures.

Authors

  • Alberto CriadoDepartamento de Matemáticas
    Facultad de Ciencia y Tecnología
    de la Universidad del País Vasco
    48080 Bilbao, Spain
    e-mail
  • Fernando SoriaDepartamento de Matemáticas and
    Instituto de Ciencias Matemáticas
    CSIC–UAM–UC3M–UCM
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
    e-mail

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