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Cesàro-type operators on Bergman–Morrey spaces and Dirichlet–Morrey spaces
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- Journal:
- Proceedings of the Edinburgh Mathematical Society , First View
- Published online by Cambridge University Press:
- 26 November 2024, pp. 1-32
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In this paper, we will show the Carleson measure characterizations for the boundedness and compactness of the Cesàro-type operator
\begin{equation*}\mathcal{C}_{\mu}(f)(z)=\sum^{\infty}_{n=0}\left( \int_{[0,1)}t^nd\mu(t)\right) \left(\sum^{n}_{k=0}a_k \right)z^n, \quad z\in \mathbb{D},\end{equation*}acting on a number of important analytic function spaces on
$\mathbb{D}$, where µ is a positive finite Borel measure. The function spaces are some newly appeared analytic function spaces (e.g., Bergman–Morrey spaces 
$A^{p,\lambda}$ and Dirichlet–Morrey spaces 
$\mathcal{D}_p^{\lambda}$) . This work continues the lines of the previous characterizations by Blasco and Galanopoulos et al. for classical Hardy spaces and weighted Bergman spaces and so forth.
