통합자연과학논문집 (Journal of Integrative Natural Science)

조선대학교 기초과학연구원 (The Basic Science Institute Chosun University)
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Sobolev Estimates for Certain Singular Curves

  • 투고 : 2011.09.27
  • 심사 : 2011.12.22
  • 발행 : 2011.12.30
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초록

In this paper we obtain some Sobolev estimates for the integral operator over singular curves (t, $t^m$) on $\mathbb{R}^2$ for $m{\geq}2$.

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과제정보

연구 과제 주관 기관 : Chosun University

참고문헌

  1. M. Christ, "Endpoint bounds for singular fractional integral operators", preprint, unpublished, 1988.
  2. M. Christ, "Failure of an endpoint estimates for integrals along curves", Fourier analysis and partial differential equations, ed. by Garcia-Cuerva, E. Hernadez, F. Soria and J.L. Torrea, CRC Press, 1995.
  3. A. Greenleaf, A. Seeger, and S. Wainger, "On X-ray transforms for rigid line complexes and integrals over curves in", Proc. Amer. Math. Soc., No. 12, pp. 3533-3545, 1999.
  4. F. Ricci and E. M. Stein, "Harmonic analysis on nilpotent groups and singular integrals III : Fractional integration along manifolds", J. Funct. Anal., Vol. 86, pp. 360-389, 1989. https://doi.org/10.1016/0022-1236(89)90057-8