## Analysis & PDE

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

### On weak weighted estimates of the martingale transform and a dyadic shift

#### 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
Revised: 10 February 2018
Accepted: 10 April 2018
First available in Project Euclid: 15 January 2019

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

#### 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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