O. Karlovych

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20232025

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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…

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

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