Generalized Cesàro operators on Dirichlet-type spaces

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

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