E. Shargorodsky

activity

20012025

most citedOn negative eigenvalues of two-dimensional Schrödinger operators

20 citations · 47 across the 23 of their papers we have counts for

collaborators

26 papers

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

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.AP2024

An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions

David Berger, René L. Schilling, Eugene Shargorodsky +1

We study the equation $m (D) f = 0$ in a large class of sub-exponentially growing functions. Under appropriate restrictions on $m \in C (R^{n})$ , we show that every such soluti…

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

Maximal Noncompactness of Wiener-Hopf Operators

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

An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions

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