  In a recent work by Cruz-Uribe et al. was obtained that
\[|\{x\in{\mathbb{R}^d}:w(x)|G(fw^{-1})(x)|>\alpha\}|\lesssim\frac{[w]_{A_1}^2}{\alpha}\int_{{\mathbb{R}^d}}|f|dx\]
both in the matrix and scalar settings, where $G$ is either the
Hardy-Littlewood maximal function or any Calder\'on-Zygmund operator. In this
note we show that the quadratic dependence on $[w]_{A_1}$ 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.
