Abstract.
We study the Lp–boundedness properties of convolution operators whose convolution kernels are obtained by adapting product kernels to curves in the plane.
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Carbery, A., Seeger, A.: Hp and Lp–variants of multiparameter Calderón– Zygmund theory. Trans. Am. Math. Soc. 334, 719–747 (1993)
Carbery, A., Wainger, S., Wright, J.: Double Hilbert transforms along polynomial surfaces in R3. Duke Math. J. 101, 499–513 (2000)
Folland, G., Stein, E.M.: Hardy Spaces on Homogeneous Groups. Princeton U. Press., Princeton, NJ, 1982
Fefferman, R., Stein, E.M.: Singular integrals on product spaces. Adv. Math. 45, 117–143 (1982)
Journé, J.L.: Calderón–Zygmund operators on product spaces. Rev. Mat. Ibero–Am. 3, 55–91 (1985)
Nagel, A., Ricci, F., Stein, E.M.: Singular integrals with flag kernels and analysis on quadratic CR manifolds. J. Funct. Anal. 181, 29–118 (2001)
Stein, E.M., Wainger, S.: Problems in harmonic analysis related to curvature. Bull. Am. Math. Soc. 84, 1239–1295 (1978)
Ricci, F., Stein, E.M.: Multiparameter singular integrals and Maximal functions. J. Ann. Inst. Fourier 42, 637–670 (1992)
Stein, E.M.: Interpolation of linear operators. Trans. Am. Math. Soc. 87, 159–172 (1958)
Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton U. Press, Princeton, NJ, 1970
Stein, E.M.: Harmonic Analysis: Real–Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton U. Press, Princeton, NJ, 1993
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in final form: 17 November 2003
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Secco, S. Adapting product kernels to curves in the plane. Math. Z. 248, 459–476 (2004). https://doi.org/10.1007/s00209-004-0664-x
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DOI: https://doi.org/10.1007/s00209-004-0664-x