Computational Methods and Function Theory 7 (2007), No. 1, 205--238
Copyright Heldermann Verlag 2007
Functions of ω-Bounded Type in the Half-Plane
email@example.com , National Academy of Sciences of Armenia, Institute of Mathematics, 24-b Marshal Baghramian Avenue, 375019 Yerevan, Armenia.
firstname.lastname@example.org , Yerevan State University, Department of Mathematics, Alex Manookian str. 1, 375049 Yerevan, Armenia.
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 Apω,γ 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 L2ω,0 to A2ω,0, a Paley-Wiener type theorem and a theorem on an explicitely written isometry between A2ω,0 and the Hardy space H2 are proved. Then a theorem on projection from the Lebesgue spaces Lpω,0 to Apω,0 is proved.
Keywords: Weighted spaces of regular functions.
MSC 2000: Primary 32A35; Secondary 31A05.
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