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We consider the Hardy space (C +) in the half-plane with an exponential weight. In this space we study the analytic continuation from the boundary. In the previous works for the case ∈ (1, 2] a result on analytic continuation from the imaginary axis was obtained, and it was a generalization of Paley-Wiener theorem. But for many applications the case = 1 is more interesting. For this case in the paper we obtain estimates for a function satisfying certain standard conditions.

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