FATOU THEOREM AND EMBEDDING THEOREMS FOR THE MEAN LIPSCHITZ FUNCTIONS ON THE UNIT BALL

Abstract

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 <TEX>$\mathbb{C}_n$</TEX>.