S. Tikhonov

activity

20162026

collaborators

Showing 2024Show all

6 papers · 1 filter

math.CA2024

Poisson summation formula in weighted Lebesgue spaces

Miquel Saucedo, Sergey Tikhonov

We characterize the parameters $(α, β, p, q)$ for which the condition $f ∣ x ∣^{α} \in L^{p}$ and $f ∣ ξ ∣^{β} \in L^{q}$ implies the validity of the Poisson summation formula, thus complet…

math.CA2024

Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces

Yurii Kolomoitsev, Sergey Tikhonov

We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results…

math.CA2024

Note on Fourier inequalities

Miquel Saucedo, Sergey Tikhonov

We prove that the Hausdorff--Young inequality $∥ f ∥_{q (\cdot)} \leq C ∥ f ∥_{p (\cdot)}$ with $q (x) = p^{'} (1/ x)$ and $p (\cdot)$ even and non-decreasing holds in variable…

math.FA2024

Sampling discretization in Orlicz spaces

Egor Kosov, Sergey Tikhonov

We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery pr…

math.CA2024

Subcritical Fourier uncertainty principles

Miquel Saucedo, Sergey Tikhonov

It is well known that if a function $f$ satisfies $∥ f (x) e^{π α ∣ x ∣^{2}} ∥_{p} + ∥ f (ξ) e^{π α ∣ ξ ∣^{2}} ∥_{q} < \infty (*)$ with $α = 1$ and $1 \leq p, q < \infty$ , the…

math.CA2024

Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter

Michael I Ganzburg, Miquel Saucedo, Sergey Tikhonov

In this paper, we study the form of the constant $C$ in the Bernstein--Nikolskii inequalities $∥ f^{(s)} ∥_{q} ≲ C (s, p, q) ∥ f ∥_{p}, 0 < p < q \leq \infty$ , for trigonom…