Poletsky-Stessin-Hardy spaces in the plane

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Abstract

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.

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• Poletsky-Stessin-Hardy spaces in the plane. (deposited 29 Sep 2013 21:58)
  • Poletsky-Stessin-Hardy spaces in the plane. (deposited 09 Sep 2014 16:11) [Currently Displayed]