  In recent work by Reguera and Thiele and by Reguera and Scurry, two
conjectures about joint weighted estimates for Calder\'on-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 Calder\'on-Zygmund operators in higher
dimensions. This allows us to fully disprove the conjectures.
