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Functions of ω-Bounded Type in the Half-Plane

Functions of ω-Bounded Type in the Half-Plane In this paper we introduce and investigate functions of ω-bounded type in the half-plane. We also investigate some properties of the Banach spaces Aω,γp which are natural subsets of functions of ω-bounded type, as Hardy classes are in Nevanlinna’s class N. The classes of δ-subharmonic functions of ω-bounded type are defined by a weighted integrability condition of Tsuji’s characteristics. The canonical representations of these classes by some Green type potentials and an analog of Poisson integral are obtained. Particularly, these representations become canonical factorizations for the corresponding meromorphic classes of ω-bounded type. A theorem on the orthogonal projection from Lω,02 to Aω,02, a Paley-Wiener type theorem and a theorem on an explicitely written isometry between Aω,02 and the Hardy space H2 are proved. Then a theorem on projection from the Lebesgue spaces Lω,0p to Aω,00 is proved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Functions of ω-Bounded Type in the Half-Plane

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Publisher
Springer Journals
Copyright
Copyright © Heldermann  Verlag 2007
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/bf03321641
Publisher site
See Article on Publisher Site

Abstract

In this paper we introduce and investigate functions of ω-bounded type in the half-plane. We also investigate some properties of the Banach spaces Aω,γp which are natural subsets of functions of ω-bounded type, as Hardy classes are in Nevanlinna’s class N. The classes of δ-subharmonic functions of ω-bounded type are defined by a weighted integrability condition of Tsuji’s characteristics. The canonical representations of these classes by some Green type potentials and an analog of Poisson integral are obtained. Particularly, these representations become canonical factorizations for the corresponding meromorphic classes of ω-bounded type. A theorem on the orthogonal projection from Lω,02 to Aω,02, a Paley-Wiener type theorem and a theorem on an explicitely written isometry between Aω,02 and the Hardy space H2 are proved. Then a theorem on projection from the Lebesgue spaces Lω,0p to Aω,00 is proved.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Apr 1, 2007

Keywords: Weighted spaces of regular functions; 32A35; 31A05

References