Estimates of $\Gamma$-functions and their $\log$-derivatives

Abstract

We provide a lower bound for a weighted ratio of $\Gamma -$functions and its $\log -$derivative. Then we apply this result to estimate the norm of the operator associated with the Cesáro operator in the Hardy space $H^p({\mathbb{C}}_{+})$, $1<p<\infty$

11 pages, 2 figures