On the composition of functions of bounded mean oscillation with meromorphic functions (Q1191305)

Let \(\Omega_ 1\) and \(\Omega_ 2\) be domains in the complex plane \(\mathbb{C}\). A function \(g: \Omega_ 1\to\Omega_ 2\) is said to preserve BMO, if for every \(f\in\text{BMO}(\Omega_ 2)\), the composition \(f\circ g\in\text{BMO}(\Omega_ 1)\). It is known that quasi-conformal mappings preserve BMO. In two previous publications the author has characterized the analytic functions preserving BMO [see the author, J. Math. Kyoto Univ. 28, No. 1, 141-152 (1988; Zbl 0683.30038); ibid. 29, No. 2, 309-315 (1989; Zbl 0701.30033)]. The present article deals with the characterization of Blaschke type meromorphic functions preserving BMO.