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Alan, M. A.; Göğüş, N. G.
Complex analysis and operator theory, 06/2014, Letnik: 8, Številka: 5Journal Article
In this paper we give two characterizations of the Poletsky–Stessin–Hardy spaces in the complex plane: First we completely describe functions in these spaces by having a harmonic majorant with a certain growth condition and we prove some basic results about these spaces. Second we describe these functions in terms of their boundary values as a weighted subclass of the usual L p class with respect to the arclength measure on the boundary, when the boundary is C 2 . In particular, we extend the classical result of Beurling which describes the invariant subspaces of the shift operator. Additionally we provide non-trivial examples.
