For the Paley-Wiener space and the weighted Hardy spaces in the half-plane we consider problems on splitting a function into a sum of two, each being "large" only in their domain. For the first space the problem is solved completely, for the second we obtain sufficient conditions of solvability.
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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