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arXiv · 1308.4881

Logarithmic convexity of area integral means for analytic functions II

Chunjie Wang·Jie Xiao·Kehe Zhu
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Abstract

For $0<p<\infty$ and $-2\le\alpha\le0$ we show that the $L^p$ integral mean on $rD$ of analytic function in the unit disk $D$ with respect to the weighted area measure $(1-|z|^2)^\alpha dA(z)$ is a logarithmically convex function of $r$ on $(0,1)$.

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Chunjie Wang, Jie Xiao, Kehe Zhu. 2013-08-22. Logarithmic convexity of area integral means for analytic functions II. https://doi.org/10.1017/s1446788714000457

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