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LOGARITHMIC CONVEXITY OF AREA INTEGRAL MEANS FOR ANALYTIC FUNCTIONS II
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 98 / Issue 1 / February 2015
- Published online by Cambridge University Press:
- 14 October 2014, pp. 117-128
- Print publication:
- February 2015
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- Article
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- You have access
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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 
$(0,1)$.
