OPERATORS ON THE BESOV SPACES OF HOLOMORPHIC FUNCTIONS ON THE UNIT BALL IN $\mathbb{C}^n$

Abstract

In the present paper we consider the Toeplitz-$T_{\bar{h}}^{ \alpha}$ and differentiation-$D^\delta $ operators on the Besov spaces $B_p(\beta)$ for all $0< p<\infty.$ We show that $T_{\bar{h}}^{ \alpha}: B_p(\beta)\rightarrow B_p(\beta)$ for $\bar h\in H^\infty(B^n)$ and $D^\delta :B_p(\beta)\rightarrow B_p(\widetilde\beta)$, where  $\widetilde\beta=\beta +p\delta .$