Muckenhoupt–Wheeden conjectures in higher dimensions
Volume 233 / 2016
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.
