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\(L^p\) and \(H^1\) Boundedness of Oscillatory Singular Integral Operators with Hölder Class Kernels

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Abstract

For oscillatory singular integrals with polynomial phases and Hölder class kernels, we establish their uniform boundedness on \(L^p\) spaces as well as a sharp logarithmic bound on the Hardy space \(H^1\). These results improve the ones in (Pan in Forum Math 31: 535–542, 2019) by removing the restriction that the phase polynomials be quadratic.

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Authors and Affiliations

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

    Yibiao Pan

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  1. Yibiao Pan
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Correspondence to Yibiao Pan.

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Pan, Y. \(L^p\) and \(H^1\) Boundedness of Oscillatory Singular Integral Operators with Hölder Class Kernels. Integr. Equ. Oper. Theory 93, 42 (2021). https://doi.org/10.1007/s00020-021-02659-z

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  • DOI: https://doi.org/10.1007/s00020-021-02659-z

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