Pacific Journal of Mathematics

$L^{p}$-boundedness of the multiple Hilbert transform along a surface.

James T. Vance, Jr.

Article information

Source
Pacific J. Math., Volume 108, Number 1 (1983), 221-241.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102720484

Mathematical Reviews number (MathSciNet)
MR709712

Zentralblatt MATH identifier
0523.44003

Subjects
Primary: 44A15: Special transforms (Legendre, Hilbert, etc.)
Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)

Citation

Vance, James T. $L^{p}$-boundedness of the multiple Hilbert transform along a surface. Pacific J. Math. 108 (1983), no. 1, 221--241. https://projecteuclid.org/euclid.pjm/1102720484


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References

  • [271] , [3,Theorem l,pg. 397], and especially [5,Theorem 3.1,pg. 243]; precedents are also found in the study of related maximal functions, as in
  • [1] E. Fabes, Singular integrals and partial differential equations of parabolic type, Studia Math., 28(1966), 81-131.
  • [2] A. Nagel, N. M Riviere, and S. Wainger, On Hilbert transforms along curves, Bull. Amer. Math. Soc, 80 (1974), 106-108.
  • [3] A. Nagel, On Hilbert transforms along curves. II, Amer. J. Math., 98 (1976), 395-403.
  • [4] A. Nagel, A maximal function associated to the curve (t, t2), Proc. Nat. Acad. Sci. U.SA., 73 (1976), 1416-1417.
  • [5] A. Nagel and S. Wainger, Hilbert transformsassociated withplane curves, Trans. Amer. Math. Soc., 223 (1976), 235-252.
  • [6] A. Nagel and S. Wainger, L2 boundedness of Hilbert transforms along surfaces and convolution operators homogeneous with respect to a multiple parameter group, Amer. J. Math., 99 (1977), 761-785.
  • [7] W. C. Nestlerode, Singular integrals and maximal functions associated with highly monotone curves, Trans. Amer. Math. Soc., 267 (1981), 435-444.
  • [8] N. M Riviere, Singular integrals and multiplier operators, Ark. Math., 9 (1971), 243-278.
  • [9] E. M. Stein, Maximal functions: homogeneous curves, Proc. Nat. Acad. Sci. U.S.A., 73 (1976), 2176-2177.
  • [10] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, NJ, 1970.
  • [11] E. M. Stein and S. Wainger, The estimation of an integral, arising in multiplier transformations, Studia Math., 35 (1970), 101-104.
  • [12] E. M. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc, 84 (1978), 1239-1295.
  • [13] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, NJ, 1971.
  • [14] R. Strichartz, Singular Integrals Supported on Submanifolds, preprint.
  • [15] David A. Weinberg, The Hilbert transform and maximal function for approximately homogeneous curves, Trans. Amer. Math. Soc, 267 (1981), 295-306.