S. Tikhonov

activity

20162026

collaborators

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3 papers · 1 filter

math.CA2025

Extremizers of a Fourier uncertainty principle related to averaging

Miquel Saucedo, Sergey Tikhonov

We study the uncertainty principle $∥ μ (ξ) ∣ ξ ∣^{β} ∥_{\infty}^{α} (\int ∣ x ∣^{α} d μ)^{β} \geq C (α, β, d) ∥ μ ∥_{T V}^{α + β}$ for finite non-negative measures…

math.CA2025

Kahane-Katznelson-de Leeuw theorem and absolute convergence of Fourier series

Miquel Saucedo, Sergey Tikhonov

We extend the Kahane-Katznelson-de Leeuw theorem to smoothness spaces by showing that for any $g \in W^{l, 2} (T^{d})$ , there exists a function $f \in C^{l} (T^{d})$ satisf…

math.CA2025

The Fourier transform is an extremizer of a class of bounded operators

Miquel Saucedo, Sergey Tikhonov

We show that, for a natural class of rearrangement admissible spaces $X$ and $Y$ , the Fourier operator is bounded between $X$ and $Y$ if and only if any operator of joint strong ty…