Generalized Cesàro operators on Dirichlet-type spaces

Abstract: In this note, we introduce and study a new kind of generalized Ces`aro operators $\mathcal{C}{\mu}$, induced by a positive Borel measure $\mu$ on $[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $\mu$ for which $\mathcal{C}{\mu}$ is bounded (compact) from one Dirichlet-type space $\mathcal{D}{\alpha}$ into another one $\mathcal{D}{\beta}$.