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arXiv · 2608.04880

Isometric Composition Operators on $BMOA$ for $0<p<\infty$

Zhaopeng Lin
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Abstract

We characterize the analytic self-maps of the unit disk inducing isometric composition operators on \(\BMOA\) with respect to the M\"obius-invariant \(H^p\) norm for \(p\ge1\) and the corresponding quasi-norm for \(0<p<1\). In particular, this gives a complete answer to Laitila's question on the characterization of isometric composition operators for the M\"obius-invariant \(H^p\) norms, while also covering the quasi-Banach range. As a consequence, the isometric property of \(C_\varphi\) is independent of the exponent \(p\in(0,\infty)\).

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Zhaopeng Lin. 2026-08-05. Isometric Composition Operators on $BMOA$ for $0<p<\infty$. https://arxiv.org/abs/2608.04880

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