Continuity and Compactness Of Generalize Volterra Type Integral Operators on Fock-Sobolev Spaces

Abstract

The study of continuity and compactness properties of Volterra type integral operator on spaces of holomorphic functions over di erent domains is a wide history. Speci cally, on Fock spaces with domain the whole complex plane, it was initiated by (Constantin, 2012) and continued by (Mengestie, 2013). In (Mengestie, 2013) and (Mengestie and Worku, 2018) the authors have considered these properties of the generalized Volterra type inte gral operators acting between Fock spaces with Gaussian weight z2 2 . Recently, (Mengestie and Takele, 2023) characterized bounded and compact generalized Volterra type integral operators on generalized Fock spaces with weight functions growing faster than the Gaus sian weight. Their result shows that the operator experiences richer bounded and compact structure in this spaces than Fock spaces with Gaussian weight. In this thesis, we stud ied these properties of generalized Volterra type integral on Fock-Sobolev spaces with weight functions growing slower than Gaussian weight. We rst characterize bounded and compact properties in terms Brezin type integral transform and then give a sim pli ed characterization. Our result shows that, the operator has similar structure when compared with Fock spaces with Gaussian weights. The results obtained in this thesis unify and extend a number of results in the area. In particular, it generalizes the results of (Mengestie, 2016), (Mengestie, 2017) and (Mengestie and Worku, 2018).