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In this paper, we study the quaternionic counterpart of complex Fock spaces$\mathfrak{F}_{\alpha}^p ( 0<p<\infty$ and for some parameter $\alpha$) ofentire slice hyperholomorphic functions in an Euclidean unit ball$\mathbb{B}^n$ in $\mathbb{H}^n.$ We also study some basic properties of thesespaces.

Quaternionic Fock space in an Euclidean unit ball $\mathbb{B}^n$