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Adapting product kernels to curves in the plane

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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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References

  1. Carbery, A., Seeger, A.: Hp and Lp–variants of multiparameter Calderón– Zygmund theory. Trans. Am. Math. Soc. 334, 719–747 (1993)

    MATH  Google Scholar 

  2. Carbery, A., Wainger, S., Wright, J.: Double Hilbert transforms along polynomial surfaces in R3. Duke Math. J. 101, 499–513 (2000)

    MathSciNet  MATH  Google Scholar 

  3. Folland, G., Stein, E.M.: Hardy Spaces on Homogeneous Groups. Princeton U. Press., Princeton, NJ, 1982

  4. Fefferman, R., Stein, E.M.: Singular integrals on product spaces. Adv. Math. 45, 117–143 (1982)

    MathSciNet  MATH  Google Scholar 

  5. Journé, J.L.: Calderón–Zygmund operators on product spaces. Rev. Mat. Ibero–Am. 3, 55–91 (1985)

    Google Scholar 

  6. 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)

    Article  MathSciNet  MATH  Google Scholar 

  7. Stein, E.M., Wainger, S.: Problems in harmonic analysis related to curvature. Bull. Am. Math. Soc. 84, 1239–1295 (1978)

    MathSciNet  MATH  Google Scholar 

  8. Ricci, F., Stein, E.M.: Multiparameter singular integrals and Maximal functions. J. Ann. Inst. Fourier 42, 637–670 (1992)

    MATH  Google Scholar 

  9. Stein, E.M.: Interpolation of linear operators. Trans. Am. Math. Soc. 87, 159–172 (1958)

    MathSciNet  MATH  Google Scholar 

  10. Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton U. Press, Princeton, NJ, 1970

  11. Stein, E.M.: Harmonic Analysis: Real–Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton U. Press, Princeton, NJ, 1993

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Correspondence to Silvia Secco.

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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

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