Poletsky-Stessin-Hardy spaces in the plane

Alan, Muhammed Ali and Göğüş, Nihat Gökhan (2014) Poletsky-Stessin-Hardy spaces in the plane. Complex Analysis and Operator Theory, 8 (5). pp. 975-990. ISSN 1661-8254 (Print) 1661-8262 (Online)

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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.
Item Type: Article
Uncontrolled Keywords: Weighted Hardy space; Shift operator
Subjects: Q Science > QA Mathematics > QA299.6-433 Analysis
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Nihat Gökhan Göğüş
Date Deposited: 09 Sep 2014 16:11
Last Modified: 02 Aug 2019 10:22
URI: https://research.sabanciuniv.edu/id/eprint/24345

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