On a criterion of belonging to the Hardy class Hp(ℂ+) up to exponential factor

Анотація

A criterion of belonging to the Hardy class $H_p(\mathbb{C}_+)$ up to factor $e^{ikz}$ is obtained. It deals with functions $f$ analytic in $\mathbb{C}_+$, having Blaschke zero-sets, and satisfying the condition $|f(z)|\le \mathrm{exp}\{|\mathrm{Im}z|^{-1}\mathrm{exp}(o(|z|))\}$,$z\to \infty$, $z\in \mathbb{C}_+$.