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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.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Qatar University, Doha, Qatar

    Hussain Al-Qassem

  2. Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA, 19010, USA

    Leslie Cheng

  3. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Yi Biao Pan

Authors
  1. Hussain Al-Qassem
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  2. Leslie Cheng
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  3. Yi Biao Pan
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Correspondence to Hussain Al-Qassem.

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Al-Qassem, H., Cheng, L. & Pan, Y.B. On the boundedness of rough oscillatory singular integrals on Triebel-Lizorkin spaces. Acta. Math. Sin.-English Ser. 27, 1881–1898 (2011). https://doi.org/10.1007/s10114-011-0410-3

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  • DOI: https://doi.org/10.1007/s10114-011-0410-3

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