Quaternionic Fock space on slice hyperholomorphic functions

In this paper, we define the quaternionic Fock spaces $\mathfrak{F}_α^p$ 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}.

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