Volterra integral operators on a family of Dirichlet-Morrey spaces

Abstract

A family of Dirichlet-Morrey spaces $\mathcal{D}_{\lambda,K}$ of functions analytic in the open unit disk $\mathbb{D}$ are defined in this paper. We completely characterize the boundedness of the Volterra integral operators $T_g$, $I_g$ and the multiplication operator $M_g$ on the space $\mathcal{D}_{\lambda,K}$. In addition, the compactness and essential norm of the operators $T_g$ and $I_g$ on $\mathcal{D}_{\lambda,K}$ are also investigated.