Boundedness and Compactness Of Generalized Integration Operators on Fock Spaces

Abstract

Different properties of Volterra-type integral operator have been studied in the past two decades on several functional spaces. In particular, on Fock spaces boundedness and compactness of the operator was studied by (Constantin, 2012) and (Mengestie, 2013). Boundedness and compactness of generalized integration operator V (n,m) g have been studied also on spaces of analytic functions defined over a unit disc by (Du et al., 2021) and (Qian and Zhu, 2021). However, it was not studied on Fock spaces. So, the purpose of this thesis is to fill this gap and study bounded and compact properties of the operator on Fock spaces. The result of this thesis generalizes the works of (Constantin, 2012) and (Mengestie, 2013).