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Norms of some singular integral operators and their inverse operators
Title: | Norms of some singular integral operators and their inverse operators |
Authors: | Nakazi, T. Browse this author | Yamamoto, T. Browse this author |
Keywords: | Singular integral operators | Hardy spaces | Hankel operators | Toeplitz operators |
Issue Date: | 1-Sep-1997 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 387 |
Start Page: | 1 |
End Page: | 28 |
Abstract: | Let a and {3 be bounded measurable functions on the unit circle T. Then the singular integral operator Sa,/3 is defined by Sa,f3f = aP+f + f3P-f, (J E L2 (T)) where P+ is an analytic projection and P_ is a co-analytic projection. In this paper, the norms of Sa,/3 and its inverse operator on the Hilbert space L2 (T) are calculated in general, using a, {3 and a + H00 Moreover, the relations between these and the norms of Hankel operators are established. As an application, in some special case in which a and /3 are nonconstant functions, the norm of Sa,/3 is calculated in a completely explicit form. If a and {3 are constant functions, then it is well known that the norm of Sa,/3 on L2 (T) is equal to max {lal, 1/31}. If a and /3 are nonzero constant functions, then it is also known that S ,{3 on L2 (T) has an inverse operator Sa-1,13whose norm is equal to max { alal-1, 1/31-1 }. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69137 |
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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