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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8357-3-2016,
author = {Alberto Criado and Fernando Soria},
title = {Muckenhoupt-Wheeden conjectures in higher dimensions},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {25-45},
zbl = {06586866},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8357-3-2016}
}
Alberto Criado; Fernando Soria. Muckenhoupt-Wheeden conjectures in higher dimensions. Studia Mathematica, Tome 233 (2016) pp. 25-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8357-3-2016/