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(ℂ₊) up to factor e^ikz is obtained. It deals with functions f analytic in >ℂ₊, having Blaschke zero-sets, and satisfying the condition |f(z)| ≤exp{|Imz|^-1exp(o(|z|))}, z→ ∞, zÎ>ℂ₊