Communications of the
Korean Mathematical Society CKMS

We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb C^n$.

Keywords: Fatou theorem, mean Lipschitz function, embedding theorems, admissible limit

MSC numbers: 32A35, 32A18, 26B35