Logarithmic Convexity of Area Integral Means for Analytic Functions
- Autores: Chunjie Wang, Kehe Zhu
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 114, Nº 1, 2014, págs. 149-160
- Idioma: inglés
- DOI: 10.7146/math.scand.a-16643
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Resumen
We show that the $L^2$ integral mean on $r\mathsf{D}$ of an analytic function in the unit disk $\mathsf{D}$ 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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