On the sharp upper bound related to the weak Muckenhoupt-Wheeden conjecture

Abstract

We construct an example showing that the upper bound $[w{]}_{A_1}\log (\mathrm{e}+[w{]}_{A_1})$ for the $L^1(w)\to L^{1,\infty }(w)$ norm of the Hilbert transform cannot be improved in general.

18 pages, 3 figures

References in corpus (2)

• On weak weighted estimates of martingale transform
• A Bellman function counterexample to the $A_1$ conjecture: the blow-up of the weak norm estimates of weighted singular operators

Cited by in corpus (2)

• Two-weight extrapolation on function spaces and applications
• Martingale transform and Square function: some weak and restricted weak sharp weighted estimates