Geodesic
Muckenhoupt–Wheeden conjectures in higher dimensions
Alberto Criado 1   ; Fernando Soria 2
1 Departamento de Matemáticas Facultad de Ciencia y Tecnología de la Universidad del País Vasco 48080 Bilbao, Spain
2 Departamento de Matemáticas and Instituto de Ciencias Matemáticas CSIC–UAM–UC3M–UCM Universidad Autónoma de Madrid 28049 Madrid, Spain
Studia Mathematica, Tome 233 (2016) no. 1, pp. 25-45 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm8357-3-2016
Keywords: recent work reguera thiele reguera scurry conjectures about joint weighted estimates calder zygmund operators hardy littlewood maximal function refuted one dimensional key ingredients these results construction weights which value hilbert transform substantially bigger maximal function work similar construction possible classical calder zygmund operators higher dimensions allows fully disprove conjectures

Alberto Criado  1   ; Fernando Soria  2

1 Departamento de Matemáticas Facultad de Ciencia y Tecnología de la Universidad del País Vasco 48080 Bilbao, Spain
2 Departamento de Matemáticas and Instituto de Ciencias Matemáticas CSIC–UAM–UC3M–UCM Universidad Autónoma de Madrid 28049 Madrid, Spain 
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Alberto Criado; Fernando Soria. Muckenhoupt–Wheeden conjectures in higher dimensions. Studia Mathematica, Tome 233 (2016) no. 1, pp. 25-45. doi: 10.4064/sm8357-3-2016

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