A Bellman function counterexample to the A1 conjecture: the blow-up of the weak norm estimates of weighted singular operators
Abstract
We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the A1 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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