Poletsky-Stessin-Hardy spaces in the plane

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Official URL: http://dx.doi.org/10.1007/s11785-013-0334-2

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 class with respect to the arclength measure on the boundary, when the boundary is . In particular, we extend the classical result of Beurling which describes the invariant subspaces of the shift operator. Additionally we provide non-trivial examples.