A. Volberg

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20242026

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math.CA2026

The Poisson Matrix $A_{2}$ characteristic and the 3/2 blow up of the Hilbert transform

Komla Domelevo, Spyridon Kakaroumpas, Stefanie Petermichl +2

Recently the matrix $A_{2}$ conjecture was disproved. Indeed, the growth of the vector Hilbert transform in the matrix weighted $L^{2} (W)$ space was shown to be at best a constant mult…

math.CA2025

A dimension-free discrete Remez-type inequality on the polytorus

Joseph Slote, Alexander Volberg, Haonan Zhang

Consider $f : I^c ◯_{K}^{n} \to C$ a function from the $n$ -fold product of multiplicative cyclic groups of order $K$ . Any such $f$ may be extended via its Fourier expansion to an a…

math.CA2024

The matrix $A_{2}$ conjecture fails, i.e. $3/2 > 1$

Komla Domelevo, Stefanie Petermichl, Sergei Treil +1

We show that the famous matrix $A_{2}$ conjecture is false: the norm of the Hilbert Transform in the space $L^{2} (W)$ with matrix weight $W$ is estimated below by $C [W]_{A_{2}}^{3/2}$ .

The Poisson Matrix A2​ characteristic and the 3/2 blow up of the Hilbert transform

A dimension-free discrete Remez-type inequality on the polytorus

The matrix A2​ conjecture fails, i.e. 3/2>1

The Poisson Matrix $A_{2}$ characteristic and the 3/2 blow up of the Hilbert transform

The matrix $A_{2}$ conjecture fails, i.e. $3/2 > 1$