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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:  1Sep1997 
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 + f3Pf, (J E L2 (T)) where P+ is an analytic projection and P_ is a coanalytic 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 Sa1,13whose norm is equal to max { alal1, 1/311 }. 
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

Submitter: 数学紀要登録作業用
