O. Karlovych

activity

20232025

collaborators

9 papers

math.FA2025

Gohberg-Krupnik Localisation for Discrete Wiener-Hopf Operators on Orlicz Sequence Spaces

Oleksiy Karlovych, Sandra Mary Thampi

Let $Φ$ be an $N$ -function whose Matuszewska-Orlicz indices satisfy $1 < α_{Φ} \leq β_{Φ} < \infty$ . Using these indices, we introduce ``interpolation friendly" classes of Fourier multipliers…

math.FA2025

Lower estimates for the norm and the Kuratowski measure of noncompactness of Wiener-Hopf type operators

Oleksiy Karlovych, Eugene Shargorodsky

Let $X (R^{n})$ be a Banach function space and $Ω \subseteq R^{n}$ be a measurable set of positive measure. For a Fourier multiplier $a$ on $X (R^{n})$ , consider t…

math.FA2025

Maximal Noncompactness of Wiener-Hopf Operators

Oleksiy Karlovych, Eugene Shargorodsky

Let $X (R)$ be a separable translation-invariant Banach function space and $a$ be a Fourier multiplier on $X (R)$ . We prove that the Wiener-Hopf operator $W (a)$ wit…

math.FA2025

On multiplier analogues of the algebra $C + H^{\infty}$ on weighted rearrangement-invariant sequence spaces

Oleksiy Karlovych, Sandra Mary Thampi

Let $X (Z)$ be a reflexive rearrangement-invariant Banach sequence space with nontrivial Boyd indices $α_{X}, β_{X}$ and let $w$ be a symmetric weight in the intersection of the…

math.FA2025

Morrey spaces over the unit circle cannot be renormed to become rearrangement-invariant

Oleksiy Karlovych, Eugene Shargorodsky

Let $1 \leq p < \infty$ and $0 < λ < 1$ . We consider the classical Morrey space $L^{p, λ} (T)$ over the unit circle $T$ . We show that there are equimeasurable functions $f,…

math.FA2024

The essential norms of Toeplitz operators with symbols in $C + H^{\infty}$ on weighted Hardy spaces are independent of the weights

Oleksiy Karlovych, Eugene Shargorodsky

Let $1 < p < \infty$ , let $H^{p}$ be the Hardy space on the unit circle, and let $H^{p} (w)$ be the Hardy space with a Muckenhoupt weight $w \in A_{p}$ on the unit circle. In 1988, Böttcher, K…

math.FA2024

On the essential norms of Toeplitz operators on abstract Hardy spaces built upon Banach function spaces

Oleksiy Karlovych, Eugene Shargorodsky

Let $X$ be a Banach function space over the unit circle such that the Riesz projection $P$ is bounded on $X$ and let $H [X]$ be the abstract Hardy space built upon $X$ . We show that…

math.FA2024

A necessary condition for the boundedness of the maximal operator on $L^{p (\cdot)}$ over reverse doubling spaces of homogeneous type

Oleksiy Karlovych, Alina Shalukhina

Let $(X, d, μ)$ be a space of homogeneous type and $p (\cdot) : X \to [1, \infty]$ be a variable exponent. We show that if the measure $μ$ is Borel-semiregular and reverse doubling, then t…

math.FA2023

Bounded compact and dual compact approximation properties of Hardy spaces: new results and open problems

Oleksiy Karlovych, Eugene Shargorodsky

The aim of the paper is to highlight some open problems concerning approximation properties of Hardy spaces. We also present some results on the bounded compact and the dual compac…

Gohberg-Krupnik Localisation for Discrete Wiener-Hopf Operators on Orlicz Sequence Spaces

Lower estimates for the norm and the Kuratowski measure of noncompactness of Wiener-Hopf type operators

Maximal Noncompactness of Wiener-Hopf Operators

On multiplier analogues of the algebra C+H∞ on weighted rearrangement-invariant sequence spaces

Morrey spaces over the unit circle cannot be renormed to become rearrangement-invariant

The essential norms of Toeplitz operators with symbols in C+H∞ on weighted Hardy spaces are independent of the weights

On the essential norms of Toeplitz operators on abstract Hardy spaces built upon Banach function spaces

A necessary condition for the boundedness of the maximal operator on Lp(⋅) over reverse doubling spaces of homogeneous type

Bounded compact and dual compact approximation properties of Hardy spaces: new results and open problems

On multiplier analogues of the algebra $C + H^{\infty}$ on weighted rearrangement-invariant sequence spaces

The essential norms of Toeplitz operators with symbols in $C + H^{\infty}$ on weighted Hardy spaces are independent of the weights

A necessary condition for the boundedness of the maximal operator on $L^{p (\cdot)}$ over reverse doubling spaces of homogeneous type