Gaussian integral means of entire functions: logarithmic convexity and concavity

Abstract

For $0<p<\infty$ and $\alpha \in (-\infty ,\infty )$ we determine when the $L^p$ integral mean on $\{z\in \mathbb{C}:|z|\le r\}$ of an entire function with respect to the Gaussian area measure $e^{-\alpha |z{|}^2}dA(z)$ is logarithmic convex or logarithmic concave.

9 pages

Cited by in corpus (1)

• Log-Convexity of Weighted Area Integral Means of $H^p$ Functions on the Upper Half-plan