Geodesic
An equivalent definition of $H^p$ spaces in~the half-plane and some applications
Sbornik. Mathematics, Tome 25 (1975) no. 1, pp. 69-76

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Classes of functions that are holomorphic for $\operatorname{Im}z>0$ and satisfy $$ \sup_{0\pi}\int_0^\infty|f(re^{it})|^p\,dr\infty,\qquad p\in(0,\infty), $$ are considered. It is proved that they coincide with the usual classes $H^p$ in the half-plane. This result is applied to an interpolation problem in $H^p$ in a strip and to the problem of basicity of exponential functions in the space $L^2$ on the line, with exponentially decreasing weight. Bibliography: 8 titles. 
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     author = {A. M. Sedletskii},
     title = {An equivalent definition of $H^p$ spaces in~the half-plane and some applications},
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     year = {1975},
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     url = {http://geodesic.mathdoc.fr/item/SM_1975_25_1_a3/}
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A. M. Sedletskii. An equivalent definition of $H^p$ spaces in~the half-plane and some applications. Sbornik. Mathematics, Tome 25 (1975) no. 1, pp. 69-76. http://geodesic.mathdoc.fr/item/SM_1975_25_1_a3/