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Oscillatory integrals for phase functions having certain degenerate critical points

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Abstract

The paper is concerned with oscillatory integrals for phase functions having certain degenerate critical points. Under a finite type condition of phase functions we show the estimate of oscillatory integrals of the first kind. The decay of the oscillatory integral depends on indices of the finite type, the spatial dimension and the symbol.

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Authors and Affiliations

  1. Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jinmyong Kim & Zheng Quan

  2. Department of Mathematics, University of Kim Il Sung, DPR Korea

    Jinmyong Kim

Authors
  1. Jinmyong Kim
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  2. Zheng Quan
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Corresponding author

Correspondence to Zheng Quan.

Additional information

This work was supported by the National Science Foundation of China (Grant No. 10671079), the Key Project of Chinese Ministry of Education (Grant No. 104126), TRAPOYT, and the Postdoctoral Science Foundation (Grant No. 20060400851)

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Kim, J., Zheng, Q. Oscillatory integrals for phase functions having certain degenerate critical points. Sci. China Ser. A-Math. 51, 474–480 (2008). https://doi.org/10.1007/s11425-007-0135-z

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  • DOI: https://doi.org/10.1007/s11425-007-0135-z

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