(A) characterization of the Bloch space

Abstract

In the setting of the unit disk, it is recently known that the following norms are equivalent: For any given p $\in$ (0, $\infty$) and $\verepsilon \in$ (0, 1), (a) $\parallel f \parallel_B$. (b) $\sup_{\verepsilon < \mid a mid < 1} \parallel f(\alpha + (1 - \mid a \mid \cdot)-f(\alpha) \parallel_p$. In this paper we generalized this to the higher dimensional space.