Logarithmic Convexity of Area Integral Means for Analytic Functions

Authors

  • Chunjie Wang
  • Kehe Zhu

DOI:

https://doi.org/10.7146/math.scand.a-16643

Abstract

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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Published

2014-01-17

How to Cite

Wang, C., & Zhu, K. (2014). Logarithmic Convexity of Area Integral Means for Analytic Functions. MATHEMATICA SCANDINAVICA, 114(1), 149–160. https://doi.org/10.7146/math.scand.a-16643

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Articles