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Inequalities for strongly singular convolution operators

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References

  1. Benedek, A., Calderón, A. P., &Panzone, R., Convolution operators on Banach space valued functions.Proc. Nat. Acad. Sci., U.S.A., 48 (1962), 356–365.

    Article  MATH  MathSciNet  Google Scholar 

  2. Calderón, A. P., Intermediate spaces and interpolation, the complex method.Studia Math., 24 (1964), 113–190.

    MATH  MathSciNet  Google Scholar 

  3. Herz, C., On the mean inversion of Fourier and Hankel transforms.Proc. Nat. Acad. Sci., U.S.A., 40 (1954), 996–999.

    Article  MATH  MathSciNet  Google Scholar 

  4. Hirschmann, I. I., On multiplier transformations.Duke Math. J., 26 (1959), 221–242.

    Article  MathSciNet  Google Scholar 

  5. Hörmander, L., Pseudo-differential operators.Proc. Symposia Pure Appl. Math., 10 (1967), 138–183.

    MATH  Google Scholar 

  6. Hunt, R., OnL(p,q) spaces.L'Enseignement Math. 12 (1966), 249–276.

    MATH  Google Scholar 

  7. Stein, E. M., Singular integrals. Harmonic functions and differentiability properties of functions of several variables.Proc. Symposia Pure Appl. Math., 10 (1967), 316–335.

    MATH  Google Scholar 

  8. — On some functions of Littlewood-Paley and Zygmund.Bull. Amer. Math. Soc., 67 (1961), 99–101.

    MATH  MathSciNet  Google Scholar 

  9. — The characterization of functions arising as potentials.Bull. Amer. Math. Soc., 67 (1961), 102–104.

    Article  MathSciNet  Google Scholar 

  10. Stein, E. M. Integrales singulieres et fonctions differentiables de plusieurs variables. Lecture notes, Faculté des Sciences d'Orsay.

  11. Stein, E. M. &Weiss, G., An extension of a theorem of Marcinkiewicz, and some of its applications.J. Math. Mech., 8 (1959), 263–284.

    MATH  MathSciNet  Google Scholar 

  12. Wainger, S., Special trigonometric series ink dimensions.Memoirs Amer. Math. Soc., 59 (1965).

  13. Watson, G. N.,Theory of Bessel functions. 2nd edition, Cambridge University Press, New York, 1962.

    Google Scholar 

  14. Zygmund, A.,Trigonometric series, I, II. Cambridge University Press, New York, 1959.

    Google Scholar 

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This work was supported by the National Science Foundation.

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Fefferman, C. Inequalities for strongly singular convolution operators. Acta Math. 124, 9–36 (1970). https://doi.org/10.1007/BF02394567

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