Eugene Shargorodsky

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20122024

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4 papers · 1 filter

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

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.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…

math.FA2017

More on the Density of Analytic Polynomials in Abstract Hardy Spaces

Alexei Karlovich, Eugene Shargorodsky

Let ${F_{n}}$ be the sequence of the Fejér kernels on the unit circle $T$ . The first author recently proved that if $X$ is a separable Banach function space on $\mathbb{T}…