arXiv subjects

H. Arroussi

Publications and source records attributed to H. Arroussi.

3 recordsLinked to original sources

arXiv2025

Composition and Volterra type operators on large Bergman spaces with rapidly decreasing weights

We characterize boundedness, compactness and Schatten class properties of generalized Volterra-type integral operators acting between large Bergman spaces $A_\omega^p$ and $A_\omega^q$ for $0 <p, q\leq \infty$. To prove our characterizations, which involve Berezin-type integral transforms, we use the Littlewood-Paley formula of Constantin and Pel\'aez and corresponding embedding theorems. Our results generalize the work on integration operators of Pau and Pel\'{a}ez in J. Funct. Anal. 259 (2010), 2727--2756.

math.FA↗

arXiv2023

Volterra-type inner derivations on Hardy spaces

A classical result of Calkin [Ann. of Math. (2) 42 (1941), pp. 839-873] says that an inner derivation $S\mapsto [T,S] = TS-ST$ maps the algebra of bounded operators on a Hilbert space into the ideal of compact operators if and only if $T$ is a compact perturbation of the multiplication by a scalar. In general, an analogous statement fails for operators on Banach spaces. To complement Calkin's result, we characterize Volterra-type inner derivations on Hardy spaces using generalized area operators and compact intertwining relations for Volterra and composition operators. Further, we characterize the compact intertwining relations for multiplication and composition operators between Hardy and Bergman spaces.

math.FA↗

arXiv2022

Generalized Volterra type integral operators on large Bergman spaces

Let $ϕ$ be an analytic self-map of the open unit disk $\mathbb{D}$ and $g$ analytic in $\mathbb{D}$. We characterize boundedness and compactness of generalized Volterra type integral operators $$GI_{(ϕ,g)}f(z)= \int_{0}^{z}f'(ϕ(ξ))\,g(ξ)\, dξ$$ and $$GV_{ (ϕ, g)}f(z)= \int_{0}^{z} f(ϕ(ξ))\,g(ξ)\, dξ, $$ acting between large Bergman spaces $A^p_ω$ and $A^q_ω$ for $0<p,q\le \infty$. To prove our characterizations, which involve Berezin type integral transforms, we use the Littlewood-Paley formula of Constantin and Peláez and establish corresponding embedding theorems, which are also of independent interest. When $ϕ(z) = z$, our results for $GV_{(ϕ,g)}$ complement the descriptions of Pau and Peláez.

math.CV↗