Logarithmic Convexity of Area Integral Means for Analytic Functions

  • Chunjie Wang
  • Kehe Zhu

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.
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
Section
Articles