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On BMOA for Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Thomas A. Metzger
Thomas A. Metzger*
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania
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Let Δ denote the unit disk in the complex plane C. The space BMO has been extensively studied by many authors (see [3] for a good exposition of this topic). Recently, the subspace BMOA (Δ) has become a topic of interest. An analytic function f, in the Hardy class H2(A), belongs to BMOA (Δ) if

(1)

where

It is known (see [3, p. 96]) that (1) is equivalent to

(2)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 5 , 01 October 1981 , pp. 1255 - 1260
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Hayman, W. K. and Pommerenke, Ch., On analytic functions of bounded mean oscillation, Bull. London Math. Soc. 10 (1978), 219–224.Google Scholar
2. Heins, M., Hardy classes on Riemann surfaces, Lecture Notes in Mathematics 98 (Springer-Verlag, Berlin, 1969).Google Scholar
3. Petersen, K., Brownian motion, Hardy spaces and bounded mean oscillation, London Math Society Lecture Notes Series 28 (Cambridge Univ. Press, Cambridge, U.K., 1977).Google Scholar
4. Pommerenke, Ch., On inclusion relations for spaces of automorphic forms, in Advances in complex function theory, Lecture Notes in Mathematics 505 (Springer-Verlag, Berlin, 1977), 92–100.Google Scholar
5. Pommerenke, Ch., Schlichte Funktionen und analytische Funktionen von Beschrdnkter Mittlerer Oszillation, Comment. Math. Helv. 52 (1977), 591–600.Google Scholar
6. Tsuji, M., Potential theory in modern function theory, (Maruzen Co. Ltd., Tokyo, 1959).Google Scholar