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LOGARITHMIC CONVEXITY OF AREA INTEGRAL MEANS FOR ANALYTIC FUNCTIONS II
Published online by Cambridge University Press: 14 October 2014
Abstract
For $0<p<\infty$ and $-2\leq {\it\alpha}\leq 0$ we show that the $L^{p}$ integral mean on $r\mathbb{D}$ of an analytic function in the unit disk $\mathbb{D}$ with respect to the weighted area measure $(1-|z|^{2})^{{\it\alpha}}\,dA(z)$ is a logarithmically convex function of $r$ on $(0,1)$.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 98 , Issue 1 , February 2015 , pp. 117 - 128
- Copyright
- Copyright © 2014 Australian Mathematical Publishing Association Inc.
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