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Norms of some singular integral operators and their inverse operators

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83533

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
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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