On Some Convexity Questions of Handelman

Abstract

We resolve some questions posed by Handelman in 1996 concerning log convex integrable functions. In particular, we give a negative answer to a question he posed concerning the integrability of $h^2(x)/h(2x)$ when $h$ is integrable and log convex and $h(n{)}^{1/n}$ converges to 1.

arXiv comment4 pages