Gaussian integral means in the Fock space

Abstract

We explore the relation between Hadamard products of two entire functions in the weighted Fock space Fγp and their integral Gaussian means. By introducing the key auxiliary function κγ,r, we show that the growth of the Gaussian means of the Hadamard product f∗ g∗ κγ,r is controlled by the growth of Gaussian means of f and g. Among several consequences of this observation, in particular, we establish the sub-multiplicative property ∥f∗g∗κ∥F1≤‖f‖F1‖g‖F1 for functions in the classical Fock space F 1.