AI 中文总结
该研究刻画了单位圆盘上诱导BMOA上等距复合算子的解析自映射，完整回答了Laitila的相关问题，还得出复合算子的等距性质与指数p∈(0,∞)无关的结论。
AI 中文摘要
我们刻画了单位圆盘上的解析自映射，这些映射在BMOA上诱导出等距复合算子，涉及p≥1时关于莫比乌斯不变H^p范数的情况，以及0<p<1时对应的拟范数情况。这完整回答了Laitila关于莫比乌斯不变H^p范数下等距复合算子刻画的问题，同时覆盖了拟巴拿赫范围。由此可得，复合算子C_φ的等距性质与指数p∈(0,∞)无关。
英文摘要
We characterize the analytic self-maps of the unit disk inducing isometric composition operators on \(\BMOA\) with respect to the Möbius-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 Möbius-invariant \(H^p\) norms, while also covering the quasi-Banach range. As a consequence, the isometric property of \(C_φ\) is independent of the exponent \(p\in(0,\infty)\).
Comments15 pages. Comments are welcome
