On the equivalence of some conditions for weighted Hardy spaces

Let G ∈ H _σ ^p (ℂ₊), where H _σ ^p (ℂ₊) is the class of functions analytic in the half plane ℂ₊ = {z: Re z > 0} and such that . In the case where a singular boundary function G is identically constant and G(z) ≠ 0 for all z ∈, ℂ₊, we establish conditions equivalent to the condition , where H ^p (ℂ₊) is the Hardy space, in terms of the behavior of G on the real semiaxis and on the imaginary axis. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1257–1263, September, 2006.