HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >

Weighted Norm Inequalities For Some Singular Integral Operators

Files in This Item:
pre347.pdf715.26 kBPDFView/Open
Please use this identifier to cite or link to this item:http://doi.org/10.14943/83493

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
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

Submitter: 数学紀要登録作業用

Export metadata:

OAI-PMH ( junii2 , jpcoar )


 

Feedback - Hokkaido University