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arXiv · 2606.08907

A non-testing characterization of bounded and compact composition operators on $\mathcal Q_p$ spaces

Bingyang Hu·Xiaojing Zhou
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Abstract

In this paper, we give symbol-only, non-testing characterizations of bounded and compact composition operators on $\mathcal Q_p$, $0<p\le 1$, via a novel dyadic trace formulation over Carleson tents for generalized $p$-Nevanlinna counting functions. Our results resolve an open question raised in Xiao's 2001 book, as well as the diagonal case of Zhao's 2009 question, a longstanding problem in the theory of $\mathcal Q_p$ spaces. As an application of our main theorems, we also obtain boundedness and compactness criteria for the $\mathcal Q_p$-Carleson measure embedding $\textrm{id}:\mathcal Q_p\to L^2(WdA)$ for weights $W$ in the Littlewood--Paley class.

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Bingyang Hu, Xiaojing Zhou. 2026-06-08. A non-testing characterization of bounded and compact composition operators on $\mathcal Q_p$ spaces. https://arxiv.org/abs/2606.08907

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