Logarithmic convexity of area integral means for analytic functions II

Published 22 Aug 2013 in math.CV and math.CA | (1308.4881v1)

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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