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Blaschke-type maps and harmonic majoration on Riemann surfaces
Published online by Cambridge University Press: 17 April 2009
Abstract
An analytic map h of type Bl from a Riemann surface R into another S, both having Greens functions, behaves well near the “boundaryr” of R. Let X stand for a family of holomorphic functions, and let f be holomorphic on S. We shall show, for several X′s, the following:
(i) f ∈ X(S) ⇔ foh ⇔ X(R);
‖foh‖ = ‖f‖.
Use is made of harmonic majoration of subharmonic functions on R and on S.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 32 , Issue 2 , October 1985 , pp. 195 - 205
- Copyright
- Copyright © Australian Mathematical Society 1985