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Hilbert type operators acting from the Bloch space into Bergman spaces

Hilbert type operators acting from the Bloch space into Bergman spaces

Abstract Let µ be a finite positive Borelmeasure on $[0,1)$ and $\alpha \gt -1$ . The generalized integral operator of Hilbert type $\mathcal {I}_{\mu_{\alpha+1}}$ is defined on the spaces $H(\mathbb{D})$ of analytic functions in the unit disc $\mathbb{D}$ as follows: \begin{equation*}\mathcal {I}_{\mu_{\alpha+1}}(f)(z)=\int_{0}^{1} \frac{f(t)}{(1-tz)^{\alpha+1}}d\mu(t),\ \ f\in H(\mathbb{D}),\ \ z\in \mathbb{D} .\end{equation*} …