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

Abstract

In the present work weighted area integral means $M_{p,\phi }(f;\mathrm{Im}z)$ are studied and it is proved that the function $y\to \log M_{p,\phi }(f;y)$ is convex in the case when $f$ belongs to a Hardy space on the upper half-plane.

24 pages

References in corpus (2)

• Logarithmic convexity of integral means for analytic functions
• Gaussian integral means of entire functions: logarithmic convexity and concavity