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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1547521447

Digital Object Identifier
doi:10.2140/apde.2018.11.2089

Mathematical Reviews number (MathSciNet)
MR3812865

Zentralblatt MATH identifier
06887470

Subjects
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

Keywords
martingale transform weak weighted estimate

Citation

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. https://projecteuclid.org/euclid.apde/1547521447


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