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28 March 2024
 
  » arxiv » 1506.4710

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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 ;
Date 15 Jun 2015
AbstractWe 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.
Source arXiv, 1506.4710
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