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Weighted Norm Inequalities For Some Singular Integral Operators
Title: | Weighted Norm Inequalities For Some Singular Integral Operators |
Authors: | Nakazi, T. Browse this author | Yamamoto, T. Browse this author |
Issue Date: | 1-Sep-1996 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 347 |
Start Page: | 1 |
End Page: | 17 |
Abstract: | For bounded Lebesgue measurable functions α, β on the unit circle, Sα,β = αP+ + βP_ is called a singular integral operator, where P + is an analytic projection and P_ is a co-analytic projection. We study one-weighted norm inequalities of Sα,β on L2(W). We introduce a class HSr of weights with r = |α-β|/||α-β||∞ in order to characterize those weights. For example, we show that Sα,β is bounded with respect to a weight W if and only if W belongs to HSr or |α-β|W ≡ 0. If r is a nonzero constant, then HSr is just a well known class of weights due to Helson and Szego. Moreover we study the Koosis type problem of two weights of Sα,β and get very simple necessary and sufficient conditions for such weights. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69097 |
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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