Geodesic
Log-convexity of weighted area integral means of Hp functions on the upper half-plane
Serdica Mathematical Journal, Tome 45 (2019) no. 2, pp. 89-120.

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In the present work weighted area integral means Mp,ϕ(f;Imz) are studied and it is proved that the function y → logMp,ϕ(f;y) is convex in the case when f belongs to a Hardy space on the upper half-plane.
Keywords: log-convexity, weighted area integral means, holomorphic function, upper halfplane 
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     author = {Stanev, Martin},
     title = {Log-convexity of weighted area integral means of {Hp} functions on the upper half-plane},
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Stanev, Martin. Log-convexity of weighted area integral means of Hp functions on the upper half-plane. Serdica Mathematical Journal, Tome 45 (2019) no. 2, pp. 89-120. http://geodesic.mathdoc.fr/item/SMJ2_2019_45_2_a0/