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Hokkaido University Preprint Series in Mathematics >
The real part of an outer function and a Helson-Szeg weight
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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