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arXiv · 1506.04710

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

F. Nazarov·A. Reznikov·V. Vasyunin·A. Volberg
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Abstract

We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture, thus strengthening the counterexamples built by Reguera--Thiele. We show a certain logarithmic blow-up for the end-point estimates of important weighted singular operators.

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F. Nazarov, A. Reznikov, V. Vasyunin, A. Volberg. 2015-06-15. A Bellman function counterexample to the $A_1$ conjecture: the blow-up of the weak norm estimates of weighted singular operators. https://arxiv.org/abs/1506.04710

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