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Norms of some singular integral operators on weighted L2 spaces

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83707

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
Helson-Szego weight
(A2)condition
Issue Date: Oct-2002
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'_ = I-I'+ · 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 Feldman-Krupnik-Yiarcus theorem. If αβ belongs to the Hardy space H00 , we give the theorem which is similar to the Feldman-Krupnik-Marcus 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

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