Geodesic
On generalization of Paley-Wiener theorem for weighted Hardy spaces
Ufa mathematical journal, Tome 5 (2013) no. 4, pp. 30-36

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We consider the Hardy space $H^p_\sigma(\mathbb{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 $p \in (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 $ p = 1 $ is more interesting. For this case in the paper we obtain estimates for a function satisfying certain standard conditions.
Keywords: weighted Hardy space, Paley-Wiener theorem, angular boundary values. 
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     author = {B. V. Vinnitskii and V. N. Dilnyi},
     title = {On generalization of {Paley-Wiener} theorem for weighted {Hardy} spaces},
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B. V. Vinnitskii; V. N. Dilnyi. On generalization of Paley-Wiener theorem for weighted Hardy spaces. Ufa mathematical journal, Tome 5 (2013) no. 4, pp. 30-36. http://geodesic.mathdoc.fr/item/UFA_2013_5_4_a2/