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INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS AS GENERIC LOG-CONVEX WEIGHTS

Part of: Holomorphic functions of several complex variables Spaces and algebras of analytic functions

Published online by Cambridge University Press:  07 August 2017

EVGUENI DOUBTSOV Open the ORCID record for EVGUENI DOUBTSOV [Opens in a new window]
EVGUENI DOUBTSOV*
Affiliation:
St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia Department of Mathematics and Mechanics, St. Petersburg State University, Universitetski pr. 28, St. Petersburg 198504, Russia email dubtsov@pdmi.ras.ru
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Abstract

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Let ${\mathcal{H}}ol(B_{d})$ denote the space of holomorphic functions on the unit ball $B_{d}$ of $\mathbb{C}^{d}$, $d\geq 1$. Given a log-convex strictly positive weight $w(r)$ on $[0,1)$, we construct a function $f\in {\mathcal{H}}ol(B_{d})$ such that the standard integral means $M_{p}(f,r)$ and $w(r)$ are equivalent for any $p$ with $0<p\leq \infty$. We also obtain similar results related to volume integral means.

Keywords

Hardy convexity theoremvolume integral meanslog-convex weight

MSC classification

Primary: 32A10: Holomorphic functions
Secondary: 30H10: Hardy spaces 32A35: $H^p$-spaces, Nevanlinna spaces 32A36: Bergman spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 88 - 93
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

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