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Oscillatory Singular Integral Operators with Hölder Class Kernels

  • Hussain Al-Qassem
  • Leslie Cheng
  • Yibiao PanEmail author
Article

Abstract

We establish the boundedness on \(L^p({\mathbb {R}}^n)\) of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calderón–Zygmund kernel K(xy) satisfying a Hölder condition. Our results also hold on weighted \(L^p\) spaces with \(A_p\) weights.

Keywords

\(L^p\) spaces Oscillatory integrals Singular integrals 

Mathematics Subject Classification

Primary 42B20 Secondary 42B35 

Notes

Acknowledgements

We thank the referees for their helpful comments.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsQatar UniversityDohaQatar
  2. 2.Department of MathematicsBryn Mawr CollegeBryn MawrUSA
  3. 3.Department of MathematicsUniversity of PittsburghPittsburghUSA

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