Analysis & PDE

  • Anal. PDE
  • Volume 11, Number 8 (2018), 2089-2109.

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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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 A1 conjecture for those operators, which stayed open after Muckenhoupt and Wheeden’s conjecture was disproved by Reguera and Thiele.

Article information

Anal. PDE, Volume 11, Number 8 (2018), 2089-2109.

Received: 31 July 2017
Revised: 10 February 2018
Accepted: 10 April 2018
First available in Project Euclid: 15 January 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42A45: Multipliers 42A61: Probabilistic methods 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35: Function spaces arising in harmonic analysis 42B37: Harmonic analysis and PDE [See also 35-XX] 47A30: Norms (inequalities, more than one norm, etc.)
Secondary: 42A50: Conjugate functions, conjugate series, singular integrals 49L20: Dynamic programming method 49L25: Viscosity solutions

martingale transform weak weighted estimate


Nazarov, Fedor; Reznikov, Alexander; Vasyunin, Vasily; Volberg, Alexander. On weak weighted estimates of the martingale transform and a dyadic shift. Anal. PDE 11 (2018), no. 8, 2089--2109. doi:10.2140/apde.2018.11.2089.

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