On the boundedness of rough oscillatory singular integrals on Triebel-Lizorkin spaces

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Abstract

We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory integrals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions.

Keywords

Oscillatory singular integral rough kernel Orlicz spaces Block spaces extrapolation Triebel-Lizorkin spaces 

MR(2000) Subject Classification

42B20 26D05 
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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011

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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