Continuity and Density Properties in Spaces $B{V}^{p,\alpha }\left({？}^d\right)$

$B{V}^{p,\alpha }\left({？}^d\right)？\left(1\le \alpha \le p\le +\infty \right)$ spaces are new classes of functions that we introduced 2017 [1]. In this paper, we give a characterization of $B{V}^{p,\alpha }\left({？}^d\right)$ spaces and establish the continuity of the translation operator and the density of the set of regular functions of class ${\mathcal{C}}^{\infty }$ in these spaces.