INTEGRAL OPERATORS WITH CLOSED RANGE ON $D_p^\alpha$ AND $\mathcal{B}_\alpha$
Rikio Yoneda · Far East Journal of Mathematical Sciences (FJMS) · 2024
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, 2023Accepted: December 20, 2023