On the composition of functions of bounded mean oscillation with meromorphic functions
Copyright policy )On the composition of functions of bounded mean oscillation with meromorphic functions
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.
Blaschke type meromorphic functions preserving BMO, quasiconformal mappings, bounded mean oscillation, 30D50, Quasiconformal mappings in the complex plane, Blaschke products, etc., 30D45, 30C99
Blaschke type meromorphic functions preserving BMO, quasiconformal mappings, bounded mean oscillation, 30D50, Quasiconformal mappings in the complex plane, Blaschke products, etc., 30D45, 30C99
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