Logarithmic convexity of integral means for analytic functions

Details Logarithmic convexity of integral means for analytic functions Logarithmic convexity of integral means for analytic functions

2011-01-15

arxiv.org/abs/1101.2998v1

Mathematics

Complex Variables

Scientific paper

We show that the $L^2$ integral mean on $r\D$ of an analytic function in the
unit disk $\D$ with respect to the weighted area measure
$(1-|z|^2)^\alpha\,dA(z)$, where $-3\le\alpha\le0$, is a logarithmically convex
function of $r$ on $(0,1)$. We also show that the range $[-3,0]$ for $\alpha$
is best possible.

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