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On weighted Hardy spaces on the unit disk

Evgeny A. Poletsky; Khim R. Shrestha — 2015

Banach Center Publications

In this paper we completely characterize those weighted Hardy spaces that are Poletsky-Stessin Hardy spaces $H_{u}^{p}$ . We also provide a reduction of $H^{\infty}$ problems to $H_{u}^{p}$ problems and demonstrate how such a reduction can be used to make shortcuts in the proofs of the interpolation theorem and corona problem.

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