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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 | | Helson-Szego weight | | (A2)condition |
| Issue Date: | Oct-2002 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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