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FRACTIONAL INTEGRAL ALONG HOMOGENEOUS CURVES IN THE HEISENBERG GROUP

김준일
대한수학회 (The Korean Mathematical Society)|2005.05|대한수학회지 (Journal of the KMS)|제42권 제3호|pp. 499-516

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주제분류수학

초록

Abstract

We obtain the type set for the fractional integral oper-ator along the curve (t; t2; ??t3) on the three dimensional Heisenberg group when ?? 6= §1=6. The proof is based on the Fourier inversion formula and the angular Littlewood-Paley decompositions in the Heisenberg group in [5].

참고문헌 (7)

  1. M. Christ, "Endpoint bounds for singular fractional integral operators" (1988), unpublished
  2. "Convolution, curvature, and combinatorics: a case study,", (19), pp.1033~1048 (1998)
  3. A. Greenleaf, S., "A On X-ray transforms for rigid line complexes and integrals over curves in R4", 127, pp.3533~3545 (1999)
  4. J. Kim, "Lp-estimate for singular integrals and maximal operators associated with °at curves on the Heisenberg group", 114, pp.555~593 (2002)
  5. D. Obelin, "Convolution estimates for some measures on curves", 99, pp.56~60 (1987)
  6. S. Secco, "Lp-improving properties of measures supported on curves on the Heisen-berg group", 132, pp.179~201 (1999)
  7. "Fractional integration along homogeneous curves in R3", 85, pp.259~270 (1999)

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