2022-12-02T03:13:49Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/692402022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116The real part of an outer function and a Helson-Szeg weightNakazi, T.Yamamoto, T.Hardy spaceouter functionHelson-Szego weight410Suppose 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69240info:doi/10.14943/83636https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69240/1/pre490.pdfHokkaido University Preprint Series in Mathematics4901132000-08-01engpublisher