O. Karlovych

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math.FA2026

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 $I^c ◯ \subseteq R^{n}$ be a measurable set of positive measure. For a Fourier multiplier $a$ on $X (R^{n})$ , consider…

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

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

Oleksiy Karlovych, Sandra Mary Thampi

Let $I^¦$ be an $N$ -function whose Matuszewska-Orlicz indices satisfy $1 < I^\pm_{I^} ¦ \leq I^_{I^}^{2} ¦ < \infty$ . Using these indices, we introduce ``interpolation friendly" classes of Fourier multip…

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 $I^\pm_{X}, I^_{X}^{2}$ and let $w$ be a symmetric weight in the intersection of t…

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 $0 < I^» < 1$ . We consider the classical Morrey space $L^{p, I^»} (T)$ over the unit circle $T$ . We show that there are equimeasurable functions $…

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, BÃ¶ttcher,…

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

Maximal Noncompactness of Wiener-Hopf Operators

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

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 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