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Hamzeh Keshavarzi

Publications and source records attributed to Hamzeh Keshavarzi.

6 recordsLinked to original sources
arXiv2023

Schatten Class Hankel Operators on Weighted Bergman Spaces induced by regular weights

In this paper, for $1\leq p<\infty$, we provide several descriptions of Schatten $p$-class Hankel operators $H_f$ and $H_{\overline{f}}$ on the weight Bergman space $A^2_ω$, in terms of a certain global and local mean oscillation of the symbol $f\in L^2_ω$, provided $ω$ is a class of regular weights. The approaches applied to rely on several classical methods, and simultaneously rely on a novel but more convenient construction associated with the atomic decomposition of $A^2_ω$.

math.FA↗
arXiv2022

Mean ergodic composition operators on $H^\infty(\mathbb{B}_n)$

In this paper, we study (uniformly) mean ergodic composition operators on $H^\infty(\mathbb{B}_n)$. Under some additional assumptions, it is shown that mean ergodic operators have norm convergent iterates in $H^\infty(\mathbb{B}_n)$, and that they are always uniformly mean ergodic.

math.FA↗
arXiv2021

Characterization of forward, vanishing, and reverse Bergman Carleson measures using sparse domination

In this paper, using a new technique from harmonic analysis called sparse domination, we characterize the positive Borel measures including forward, vanishing, and reverse Bergman Carleson measures. The main novelty of this paper is determining the reverse Bergman Carleson measures which have remained open from the work of Luecking [Am. J. Math. 107 (1985) 85-111]. Moreover, in the case of forward and vanishing measures, our results extend the results of [J. Funct. Anal. 280 (2021), no. 6, 108897, 26 pp] from $1\leq p\leq q< 2p$ to all $0<p\leq q<\infty$. In a more general case, we characterize the positive Borel measures $μ$ on $\mathbb{B}$ so that the radial differentiation operator $R^{k}:A_ω^p(\mathbb{B})\rightarrow L^q(\mathbb{B},μ)$ is bounded and compact. Although we consider the weighted Bergman spaces induced by two-side doubling weights, the results are new even on classical weighted Bergman spaces.

math.FA↗
arXiv2021

Interpolating Sequences for Weighted Bergman Spaces on Strongly Pseudoconvex Bounded Domains

Let $0 -1$, and $Ω$ be a strongly pseudoconvex bounded domain with a smooth boundary in $\mathbb{C}^n$. We will study the interpolation problem for weighted Bergman spaces $A^p_β(Ω)$. In the case, $1\leq p<\infty$, and $β> \max \{n(2p-1)-1, n(2q-1)-1\}$, where $q$ is the conjugate exponent of $p$ (let $q=1$, for $p=1$), we show that a sequence in $\mathbb{B}_n$, the unit ball in $\mathbb{C}^n$, is interpolating for $A^p_β(\mathbb{B}_n)$ if and only if it is separated.

math.CV↗
arXiv2020

Some applications of interpolating sequences for Banach spaces of analytic functions

M. J. Beltrán-Meneua et al. \cite{beltran1} and E. Jordá and A. Rodríguez-Arenas \cite{jorda} characterized the (uniformly) mean ergodic composition operators on $H^\infty(\mathbb{D})$ and $H^\infty_ν(\mathbb{D})$, respectively. In this paper, by using the interpolating sequences, we give other necessary and sufficient conditions for the (uniformly) mean ergodicity of composition operators on these spaces.

math.FA↗