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

Nakazi, T.; Yamamoto, T.

Hokkaido University Preprint Series in Mathematics, 2000, 490, 1-13

Permalink : https://doi.org/10.14943/83636

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アクセス権	open access
DOI	https://doi.org/10.14943/83636
URI	https://hdl.handle.net/2115/69240
タイトル	The real part of an outer function and a Helson-Szeg weight
著者	著者名 Nakazi, T.
著者	著者名 Yamamoto, T.
言語	英語
キーワード	Hardy space
	outer function
	Helson-Szego weight
発行日	2000-08-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	490
ページ	1-13
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record