Quaternionic Fock space on slice hyperholomorphic functions

Abstract

In this paper, we define the quaternionic Fock spaces ${\mathfrak{F}}_{\alpha }^p$ of entire slice hyperholomorphic functions in a quaternionic unit ball $\mathbb{B}$ in $\mathbb{H}.$ We also study growth estimate and various results of entire slice regular functions in these spaces. The work of this paper is motivated by the recent work of \cite{alpa12} and \cite{marco}.