Hilbert transforms associated with plane curves. (English) Zbl 0341.44005


44A15 Special integral transforms (Legendre, Hilbert, etc.)
42A50 Conjugate functions, conjugate series, singular integrals
42A45 Multipliers in one variable harmonic analysis
42B25 Maximal functions, Littlewood-Paley theory
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[1] Alexander Nagel and Stephen Wainger, \?² boundedness of Hilbert transforms along surfaces and convolution operators homogeneous with respect to a multiple parameter group, Amer. J. Math. 99 (1977), no. 4, 761 – 785. · Zbl 0374.44003
[2] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. · Zbl 0207.13501
[3] Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. · Zbl 0232.42007
[4] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. · Zbl 0085.05601
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