. In the recent work [Cruz-Uribe et al. (2021)] it was obtained that
|{x ∈ R
d
: w(x)|G(f w−1
)(x)| > α}| ≲
[w]
2
A1
α
Z
Rd
|f |dx
both in the matrix and scalar settings, where G is either the Hardy–Littlewood maximal function or any
Calderón–Zygmund operator. In this note we show that the quadratic dependence on [w]A1
is sharp. This
is done by constructing a sequence of scalar-valued weights with blowing up characteristics so that the
corresponding bounds for the Hilbert transform and maximal function are exactly quadratic.
