Integral means, bounded mean oscillation, and Gelfer functions

Author:
Daniel Girela

Journal:
Proc. Amer. Math. Soc. **113** (1991), 365-370

MSC:
Primary 30C80; Secondary 30D50

DOI:
https://doi.org/10.1090/S0002-9939-1991-1065948-0

MathSciNet review:
1065948

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Abstract | References | Similar Articles | Additional Information

Abstract: A Gelfer function is a holomorphic function in the unit disc such that and for all in . The family of Gelfer functions contains the family of holomorphic functions in with and Re in . Yamashita has recently proved that if is a Gelfer function then while and . In this paper we prove that the function is extremal for a very large class of problems about integral means in the class . This result in particular implies that , and we use it also to obtain a new proof of a generalization of Yamashita's estimation of the BMOA norm of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1065948-0

Keywords:
Integral means,
bounded mean oscillation,
Gelfer functions,
symmetrization

Article copyright:
© Copyright 1991
American Mathematical Society