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INTEGRAL OPERATORS WITH CLOSED RANGE ON $D_p^\alpha$ AND $\mathcal{B}_\alpha$
Keywords:
integral operator, weighted Dirichlet space, weighted Bloch space, Bergman space, closed range, bounded below.DOI:
https://doi.org/10.17654/0972087124005Abstract
We study the relation between Volterra type integral operators $T_g$ with closed range on the weighted Dirichlet spaces $D_p^\alpha$ and $T_g$ with closed range on the weighted Bloch spaces $\mathcal{B}_\alpha$.
For $\alpha>0, \quad p \geq 1$, the following are equivalent for a $g$ in the Bloch space:
(1) $T_g$ is bounded below on $\mathcal{D}_p^{p(\alpha+1)}$.
(2) $T_g$ is bounded below on $L_a^p$.
(3) $T_g$ is bounded below on $\mathcal{B}_{\alpha+1}$.
Received: October 26, 2023
Accepted: December 20, 2023
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