AI 中文总结
本文针对面积Nevanlinna空间上的度量有界Volterra型算子的符号类精确刻画问题，通过建立该空间的Littlewood-Paley型刻画，得出$J_g$对应$g$属于Bloch空间、$I_g$对应$g$属于$H^\infty$的结论，解决了该领域的公开问题。
AI 中文摘要
本文研究面积Nevanlinna空间$N_\alpha^p$上的度量有界Volterra型算子$J_g$和$I_g$，其中$1\le p<\infty$且$\alpha>-1$。Choe、Koo和Smith在文献[CKS]中得到了对应符号类的部分刻画，但精确刻画仍未解决。我们建立了$N_\alpha^p$的Littlewood-Paley型刻画，并利用它肯定地解决了该问题。更准确地说，$J_g$在$N_\alpha^p$上度量有界当且仅当$g$属于Bloch空间$\mathcal{B}$，而$I_g$在$N_\alpha^p$上度量有界当且仅当$g\in H^\infty$。
英文摘要
In this paper, we study metrically bounded Volterra-type operators $J_g$ and $I_g$ on the area Nevanlinna spaces $N_α^p$, where $1\le p<\infty$ and $α>-1$. 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 $N_α^p$ and use it to resolve this problem affirmatively. More precisely, $J_g$ is metrically bounded on $N_α^p$ if and only if $g$ belongs to the Bloch space $\mathcal B$, while $I_g$ is metrically bounded on $N_α^p$ if and only if $g\in H^\infty$.
