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The real part of an outer function and a Helson-Szeg weight

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83636

Title: The real part of an outer function and a Helson-Szeg weight
Authors: Nakazi, T. Browse this author
Yamamoto, T. Browse this author
Keywords: Hardy space
outer function
Helson-Szego weight
Issue Date: 1-Aug-2000
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 490
Start Page: 1
End Page: 13
Abstract: Suppose F is a nonzero function in the Hardy space H1. We study the set {f ; f is outer and !Fl ::; Re f a.e. on 8D} where 8D is a unit circle. When F is a strongly outer function in H1 and 'Y is a positive constant, we describe the set {! ; f is outer, IFI ::; 'Y Re f and IF-1 I ::; 'Y Re u-1) a.e. on 8D}. Suppose w is a Helson-Szego weight. As an application, we parametrize real valued functions v in L∞(∂D) such that the difference between log W and the harmonic conjugate function v_*_ of v belongs to L∞(∂D) and llvll∞ is strictly less than π/2 using a contractive function α in H∞ such that (1+α)/(1-α) is equal to the Herglotz integral of W.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69240
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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