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On weak weighted
estimates of the martingale transform and a dyadic shift
Fedor Nazarov, Alexander Reznikov, Vasily Vasyunin and Alexander Volberg |
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Vol. 11 (2018), No. 8, 2089–2109
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DOI: 10.2140/apde.2018.11.2089
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Abstract |
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We consider weak-type estimates for several singular operators using the Bellman-function approach. In particular, we consider a concrete dyadic shift. We disprove the conjecture for those operators, which stayed open after Muckenhoupt and Wheeden’s conjecture was disproved by Reguera and Thiele. |
Keywords
martingale transform, weak weighted estimate
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Mathematical Subject Classification 2010
Primary: 42A45, 42A61, 42B20, 42B35, 42B37, 47A30
Secondary: 42A50, 49L20, 49L25
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Milestones
Received: 31 July 2017
Revised: 10 February 2018
Accepted: 10 April 2018
Published: 6 June 2018
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Authors |
| Fedor Nazarov | |
| Department of Mathematical
Sciences Kent State University Kent, OH United States |
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| Alexander Reznikov | |
| Department of Mathematics Michigan State University East Lansing, MI United States |
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| Vasily Vasyunin | |
| V. A. Steklov Mathematical
Institute St. Petersburg Russia |
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| Alexander Volberg | |
| Department of Mathematics Michigan State University East Lansing, MI United States |
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