On generalized Volterra type integral operators acting between Fock-Sobolev spaces

Document Type : Original Article

Authors

Mafuz Worku

Mohammed Abdella

Department of Mathematics, Jimma University, Ethiopia

10.22034/kjm.2025.494646.3406

Abstract

Recently, Mengestie and Takele characterized the bounded and compact properties of the generalized Volterra-type integral operator on weighted Fock spaces with weight functions growing faster than the Gaussian function defining the classical Fock spaces. Their result shows that the operator exhibits a richer bounded and compact structure when it acts between these spaces than the classical Fock spaces counterpart. A next question to raise is: what will happen to these properties if the weight function grows slower than the Gaussian weight function, specifically in the Fock-Sobolev spaces?
So, the aim of this paper is to study the bounded and compact properties of the generalized Volterra-type integral operator on Fock-Sobolev spaces, with the goal of investigating the effects of slower growth of the weight function on these properties. Unlike the fast-growing case, our result shows that the operator has a similar bounded and compact structure as in the classical Fock spaces.

Keywords

Fock-Sobolev spaces

Fock spaces

generalized Volterra type integral operator

Subjects

• 47 Operator theory

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