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Averages of holomorphic mappings

Published online by Cambridge University Press:  24 October 2008

V. Nestoridis
V. Nestoridis
Affiliation:
Department of Mathematics, University of Crete, Heraklion, Crete
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Extract

In this paper we present two versions in several variables of the following result:

Theorem 1([2, 3]). Let f be a function in the disc algebra (more generally in H1). Then for every point z0 in the open unit disc, there is an interval I on the unit circle T such that f(z0) = 1/|I| ∫Ifdσ, where 0 < |I| ≤ 2π denotes the length of I and σ the Lebesgue measure on T.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 2 , September 1986 , pp. 371 - 381
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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