S. Astashkin

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20242026

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5 papers · 1 filter

math.FA2026

Rigidity of sets of independent functions in symmetric spaces

Sergey V. Astashkin, Yu. V. Malykhin

We say that a symmetric function space $X$ has the $(I R)$ property whenever all sets of $N$ independent mean zero functions $f_{1}, \dots, f_{N} \in X$ , $∥ f_{k} ∥_{X} \geq 1$ , are poorly appr…

math.FA2025

On extreme points of the unit ball of a Hardy-Lorentz space

Sergey V. Astashkin

We investigate the problem of a characterization of extreme points of the unit ball of a Hardy-Lorentz space $H (I^ (I ¨ ))$ , posed by Semenov in 1978. New necessary and sufficient con…

math.FA2025

Looking for a continuous version of Bennett--Carl theorem

Sergey V. Astashkin, Karol LeÅnik, MichaÅ Wojciechowski

We study absolute summability of inclusions of r.i. function spaces. It appears that such properties are closely related, or even determined by absolute summability of inclusions o…

math.FA2024

On subspaces of Orlicz spaces spanned by independent copies of a mean zero function

Sergey V. Astashkin

We study subspaces of Orlicz spaces $L_{M}$ spanned by independent copies $f_{k}$ , $k = 1, 2, \dots$ , of a function $f \in L_{M}$ , $\int_{0}^{1} f (t) d t = 0$ . Any such a subspace $H$ is isomorphic…

math.FA2024

On the set of extreme points of the unit ball of a Hardy-Lorentz space

Sergey V. Astashkin

We prove that every measurable function $f : [0, a] \to C$ such that $∣ f ∣ = 1$ a.e. on $[0, a]$ is an extreme point of the unit ball of the Lorentz space $I^ (I ¨ )$ on $[0, a]$ whe…