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arXiv · 2608.25307

Metrically bounded Volterra-type operators on area Nevanlinna spaces

Zixing Yuan
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Abstract

In this paper, we study metrically bounded Volterra-type operators $J_g$ and $I_g$ on the area Nevanlinna spaces $N_\alpha^p$, where $1\le p<\infty$ and $\alpha>-1$. Choe, Koo and Smith \cite{CKS} obtained partial characterizations of the corresponding symbol classes, but the exact characterization was still open. We establish a Littlewood--Paley type characterization of $N_\alpha^p$ and use it to resolve this problem affirmatively. More precisely, $J_g$ is metrically bounded on $N_\alpha^p$ if and only if $g$ belongs to the Bloch space $\mathcal B$, while $I_g$ is metrically bounded on $N_\alpha^p$ if and only if $g\in H^\infty$.

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Zixing Yuan. 2026-08-26. Metrically bounded Volterra-type operators on area Nevanlinna spaces. https://arxiv.org/abs/2608.25307

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