On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane - Vynnyts’kyi, B. V.; Sharan, V.L. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We obtain the description of the zeros, singular boundary functions, and modules of angular boundary values of the functions f eq 0 which are analytic in the half-plane C_+ = { z : z > 0 } and satisfy the condition ( ε > 0 ) ( c_1 > 0 ) (z Ñ_+ ): | f ( z ) | ≤ c_1 ( (σ + ε) | z η ( | z | ) ), , where 0 ≤ σ < +∞ is a given number and η is a positive function continuously differentiable on [0; +∞ and such that tη’(t)/η(t) → 0 as t → + ∞/