Muckenhoupt-Wheeden conjectures in higher dimensions

Alberto Criado; Fernando Soria

Studia Mathematica (2016)

  • Volume: 233, Issue: 1, page 25-45
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Alberto Criado, and Fernando Soria. "Muckenhoupt-Wheeden conjectures in higher dimensions." Studia Mathematica 233.1 (2016): 25-45. <http://eudml.org/doc/285535>.

@article{AlbertoCriado2016,
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.},
author = {Alberto Criado, Fernando Soria},
journal = {Studia Mathematica},
keywords = {maximal operator; Calder'on-Zygmund operators; weighted inequalities},
language = {eng},
number = {1},
pages = {25-45},
title = {Muckenhoupt-Wheeden conjectures in higher dimensions},
url = {http://eudml.org/doc/285535},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Alberto Criado
AU - Fernando Soria
TI - Muckenhoupt-Wheeden conjectures in higher dimensions
JO - Studia Mathematica
PY - 2016
VL - 233
IS - 1
SP - 25
EP - 45
AB - 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.
LA - eng
KW - maximal operator; Calder'on-Zygmund operators; weighted inequalities
UR - http://eudml.org/doc/285535
ER -

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