In this note, we introduce and study a new kind of generalized Cesàro operator, $\mathcal{C}_{\mu}$, induced by a positive Borel measure $\mu$ on $[0, 1)$ between 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, $\mathcal{D}_{\beta}$.
Jianjun JIN
,
Shuan TANG
. GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES[J]. Acta mathematica scientia, Series B, 2022
, 42(1)
: 212
-220
.
DOI: 10.1007/s10473-022-0111-2
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