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A VAN DER CORPUT TYPE LEMMA FOR OSCILLATORY INTEGRALS WITH HÖLDER AMPLITUDES AND ITS APPLICATIONS

  • Al-Qassem, Hussain (Department of Mathematics and Physics Qatar University) ;
  • Cheng, Leslie (Department of Mathematics Bryn Mawr College) ;
  • Pan, Yibiao (Department of Mathematics University of Pittsburgh)
  • Received : 2020.03.25
  • Accepted : 2020.11.05
  • Published : 2021.03.01

Abstract

We prove a decay estimate for oscillatory integrals with Hölder amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.