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INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS AS GENERIC LOG-CONVEX WEIGHTS

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

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 [email protected]
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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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