On weak weighted estimates of martingale transform

Abstract

We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture of Muckenhoupt, which stayed open after Muckenhoupt--Wheeden's conjecture was disproved by Reguera--Thiele.

25 pages

References in corpus (1)

• 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 (3)

• Weighted norm inequalities for rough singular integral operators
• On the sharp upper bound related to the weak Muckenhoupt-Wheeden conjecture
• Two-weight extrapolation on function spaces and applications