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In complex analysis, the Hardy spaces are spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz, who named them after G. H. Hardy, because of the paper. In real analysis Hardy spaces are spaces of distributions on the real n-space , defined as boundary values of the holomorphic functions. Hardy spaces are related to the Lp spaces. For these Hardy spaces are subsets of spaces, while for the spaces have some undesirable properties, and the Hardy spaces are much better behaved. Hence, spaces can be considered extensions of spaces.
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