We characterize the holomorphic self‐maps of the unit disk for which the corresponding composition operator is an isometry of BMOA equipped with the Möbius invariant $H^p$ norm, answering a question posed by Laitila, for $p\in [1,2)$. Also, we show that the image of the symbol of an isometric composition operator for BMOA, with respect to the Möbius invariant $H^p$ norm, $p\in [1,+\infty )$, covers the whole unit disc except a set of zero logarithmic capacity.

中文翻译：

---

BMOA的Möbius不变Hp范数的等距成分算子

我们描述了单位圆盘的全纯自映射，其对应的合成算子是配备了Möbius不变量的BMOA的等轴测图 $H^p$ 规范，回答Laitila提出的问题， $p\in [\mathrm{1个}，\mathrm{2个}）$。同样，我们证明了关于BMOA的等距合成算符的符号图像，关于Möbius不变量$H^p$ 规范， $p\in [\mathrm{1个}，+\infty ）$覆盖整个单位光盘，但一组零对数容量除外。