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Blaschke-type maps and harmonic majoration on Riemann surfaces

Published online by Cambridge University Press:  17 April 2009

Shinji Yamashita
Shinji Yamashita
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Fukasawa, Setagaya, Tokyo 158, Japan.
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Abstract

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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

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