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THE RATE OF INCREASE OF MEAN VALUES OF FUNCTIONS IN HARDY SPACES

Part of: Holomorphic functions of several complex variables

Published online by Cambridge University Press:  01 April 2009

JAVAD MASHREGHI
JAVAD MASHREGHI*
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec, QC, Canada G1V OA6 (email: [email protected])
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Abstract

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The norm of a function f in the Hardy space Hp(𝔻) is by definition the limit of as r→1. We show that grows at most like o(1/log r) as r→1.

Keywords

Hardy spaceintegral meansBMO

MSC classification

Secondary: 32A35: $H^p$-spaces, Nevanlinna spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 2 , April 2009 , pp. 199 - 204
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Fefferman, C., ‘Characterizations of bounded mean oscillation’, Bull. Amer. Math. Soc. 77 (1971), 587–588.Google Scholar
[2]Fefferman, C. and Stein, E., ‘H p spaces of several variables’, Acta Math. 129 (1972), 137–193.CrossRefGoogle Scholar
[3]Hardy, G. H., ‘The mean values of the modulus of an analytic function’, Proc. London Math. Soc. 14 (1915), 269–277.Google Scholar
[4]Koosis, P., Introduction to H p Spaces, 2nd edn, Cambridge Tracts in Mathematics (Cambridge University Press, Cambridge, 1998).Google Scholar