Isometries of composition operators on BMOA
Tiantian Chen, Hasi Wulan · Proceedings of the American Mathematical Society · 2024
We characterize completely the analytic self-maps of the unit disc inducing isometric composition operators on the space BMOA equipped with a Möbius invariant H p H^p norm. Our results answer a question raised by J. Laitila [Math. Nachr. 283(2010), pp. 1646–1653] for all 1 ≤ p > ∞ 1\leq p>\infty , which extends a result of S. Pouliasis [Bull. London Math. Soc. 53(2021), pp. 458–469] from 1 ≤ p > 2 1\leq p>2 to 1 ≤ p ≤ 4 1\leq p\le 4 . Meanwhile, we generalize the result of Laitila from p = 2 p=2 to 1 ≤ p ≤ 4 1\leq p\le 4 and we also show that the parameter p = 4 p=4 is the best possible.