Article

Positivity

, Volume 13, Issue 2, pp 339-366

A bilinear oscillatory integral along parabolas

  • Dashan FanAffiliated withDepartment of Mathematics, University of Wisconsin-Milwaukee & Huazhong Normal University Email author 
  • , Xiaochun LiAffiliated withDepartment of Mathematics, University of Illinois at Urbana-Champaign

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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