Výsledky vyhledávání - "Karlovych, Oleksiy"

Report

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

Autor: Karlovych, Oleksiy, Shargorodsky, Eugene

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 the essential norm of the Toeplitz operator $T(a):H[X]\to H[X]$ coinc

Externí odkaz: http://arxiv.org/abs/2408.13907

Zobrazit plný text záznamu

Report

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

Autor: Karlovych, Oleksiy, Shalukhina, Alina

Let $(X,d,\mu)$ be a space of homogeneous type and $p(\cdot):X\to[1,\infty]$ be a variable exponent. We show that if the measure $\mu$ is Borel-semiregular and reverse doubling, then the condition ${\rm ess\,inf}_{x\in X}p(x)>1$ is necessary for the

Externí odkaz: http://arxiv.org/abs/2403.10915

Zobrazit plný text záznamu

Report

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

Autor: Karlovych, Oleksiy, Shargorodsky, Eugene

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 compact approximation properties (shortly, BCAP and DCAP) of such spaces, to

Externí odkaz: http://arxiv.org/abs/2308.04072

Zobrazit plný text záznamu