Analysis & PDE
- Anal. PDE
- Volume 11, Number 8 (2018), 2089-2109.
On weak weighted estimates of the martingale transform and a dyadic shift
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.
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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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
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