Article
Ufa Mathematical Journal
Volume 5, Number 4, pp. 30-36
On generalization of Paley-Wiener theorem for weighted Hardy spaces
Dilnyi V.N., Vinnitskii B.V.
DOI:10.13108/2013-5-4-30
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We consider the Hardy space $H^p_\sigma(\mathds{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.