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INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS AS GENERIC LOG-CONVEX WEIGHTS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 97 / Issue 1 / February 2018
- Published online by Cambridge University Press:
- 07 August 2017, pp. 88-93
- Print publication:
- February 2018
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- Article
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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.
