Generalized Cesàro operators on Dirichlet-type spaces

Abstract

In this note, we introduce and study a new kind of generalized Cesàro 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 ${\mathcal{D}}_{\beta }$.

Accepted by Acta Mathematica Scientia