Gaussian integral means of entire functions: logarithmic convexity and concavity

For $0<p<\infty$ and $α\in (-\infty,\infty)$ 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 $e^{-α|z|^2}\,dA(z)$ is logarithmic convex or logarithmic concave.

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