Positivity

, Volume 13, Issue 2, pp 339–366

A bilinear oscillatory integral along parabolas

Article

DOI: 10.1007/s11117-008-2270-3

Cite this article as:
Fan, D. & Li, X. Positivity (2009) 13: 339. doi:10.1007/s11117-008-2270-3

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 operatoroscillatory integral

Mathematics Subject Classification (2000)

Primary 42B20, 42B25Secondary 46B70, 47B38

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