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Norms of some singular integral operators on weighted L2 spaces
Title:  Norms of some singular integral operators on weighted L2 spaces 
Authors:  Nakazi, T. Browse this author  Yamamoto, T. Browse this author 
Keywords:  Singular integral operator  Norm  Hardy space  HelsonSzego weight  (A2)condition 
Issue Date:  Oct2002 
Journal Title:  Hokkaido University Preprint Series in Mathematics 
Volume:  562 
Start Page:  1 
End Page:  27 
Abstract:  Let α and β be measurable functions on the unit circle T, and let W be a positive function on T such that the Ricsz projection P+ is bounded on the weighted space L2(W) on T. The singular integral operator Sa,/3 is defined by Sa,f3f = nI'+f + pI'_f, (f E L2 (W)) where I'_ = II'+ · Leth be an outer function such that TV= 1h12 , and let cp be an unimodular function such that cp = Ti/h. In this paper, the norm of Sa ,rJ on L2 (TV) is calculated in general, using α,β and cp. Moreover, if o; and (} are constant functions, then we give the another proof of the FeldmanKrupnikYiarcus theorem. If αβ belongs to the Hardy space H00 , we give the theorem which is similar to the FeldmanKrupnikMarcus theorem. 
Type:  bulletin (article) 
URI:  http://hdl.handle.net/2115/69311 
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
