A. Volberg

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20242026

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math.FA2026

Dimension-free bounds for Riesz transforms on the Hamming cube via a Bellman function

Komla Domelevo, Paata Ivanisvili, Stefanie Petermichl +1

We give a Bellman-function proof of the dimension-free estimate \[ \Big\| \vec{R} f \Big\|_{L^p(Î©;\,\ell^2)} \lesssim (p-1) \,\|f\|_{L^p(Î©)}, \qquad 2\le p<\infty, \] for the vec…

math.FA2024

Dimension-free discretizations of the uniform norm by small product sets

Lars Becker, Ohad Klein, Joseph Slote +2

Let $f$ be an analytic polynomial of degree at most $K - 1$ . A classical inequality of Bernstein compares the supremum norm of $f$ over the unit circle to its supremum norm over the…

math.FA2024

Bohnenblust--Hille inequality for cyclic groups

Joseph Slote, Alexander Volberg, Haonan Zhang

For any $K > 2$ and the multiplicative cyclic group $I^c ◯_{K}$ of order $K$ , consider any function $f : I^c ◯_{K}^{n} \to C$ and its Fourier expansion $f(z)=\sum_{Î±\in\{0,1,\ldots,K-1\}^n…