Muckenhoupt-Wheeden conjectures in higher dimensions
Criado, Alberto · Soria, Fernando
Original · EN
In recent work by Reguera and Thiele and by Reguera and Scurry, two conjectures about joint weighted estimates for Calderón-Zygmund operators and the Hardy-Littlewood maximal function have been refuted in the one-dimensional case. One of the key ingredients for these results is the construction of weights for which the action 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.
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