On the sharpness of some quantitative Muckenhoupt–Wheeden inequalities - Lerner, Andrei K. (2024)
In the recent work [Cruz-Uribe et al. (2021)] it was obtained that both in the matrix and scalar settings, where is either the Hardy–Littlewood maximal function or any Calderón–Zygmund operator. In this note we show that the quadratic dependence on 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.