Positivity

, Volume 13, Issue 2, pp 339–366 | Cite as

A bilinear oscillatory integral along parabolas

Article

Abstract

We establish an \(L^\infty \times L^2 \rightarrow L^2\) norm estimate for a bilinear oscillatory integral operator along parabolas incorporating oscillatory factors \(e^{i|t|^{-\beta}}\).

Keywords

Bilinear operator oscillatory integral 

Mathematics Subject Classification (2000)

Primary 42B20, 42B25 Secondary 46B70, 47B38 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Wisconsin-Milwaukee & Huazhong Normal UniversityMilwaukeeUSA
  2. 2.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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