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Characterisations for analytic functions of bounded mean oscillation

Published online by Cambridge University Press:  17 April 2009

Jie Miao
Jie Miao
Affiliation:
Department of Mathematics, Hangzhou University Hangzhou, Zhejiang, People's Republic of China
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Abstract

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Let α > 0 and let f[α](z) be the αth fractional derivative of an analytic function f on the unit disc D. In this paper we show that f ∈ BMOA if and only if |f[α](z)|2 (l - |z|2)2α−1dA(z) is a Carleson measure and f ∈ VMOA if and only if |f[α](z)|2 (1 − |z|2)2α−1dA(z) is a vanishing Carleson measure, where A denotes the normalised Lebesgue measure on D. Hence a significant extension of familiar characterisations for analytic functions of bounded and vanishing mean oscillation is obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 1 , August 1992 , pp. 115 - 125
Copyright
Copyright © Australian Mathematical Society 1992

References

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