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Order functions of plurisubharmonic functions

Halil CelikEvgeny Poletsky — 1997

Studia Mathematica

We consider the following problem: find on 2 a plurisubharmonic function with a given order function. In particular, we prove that any positive ambiguous function on 1 which is constant outside a polar set is the order function of a plurisubharmonic function.

On weighted Hardy spaces on the unit disk

Evgeny A. PoletskyKhim 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 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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