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H p spaces of several variables

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References

  1. Burkholder, D. L. & Gundy, R. F., Distribution function inequalities for the area integral. To appear in Studia Math.

  2. Burkholder, D. L., Gundy, R. F. &Silverstein, M. L., A maximal function characterization of the classH p.Trans. Amer. Math. Soc., 157 (1971), 137–153.

    Article  MathSciNet  MATH  Google Scholar 

  3. Calderón, A. P., Commutators of singular integral operators.Proc. Nat. Acad. Sci. U.S.A., 53 (1965), 1092–1099.

    MATH  MathSciNet  Google Scholar 

  4. —, Intermediate spaces and interpolation, the complex method.Studia Math., 24 (1964), 113–190.

    MATH  MathSciNet  Google Scholar 

  5. Calderón, A. P. &Zygmund, A., On the existence of certain singular integrals.Acta Math., 88 (1952), 85–139.

    MathSciNet  MATH  Google Scholar 

  6. —, On higher gradients of harmonic functions.Studia Math., 24 (1964), 211–226.

    MathSciNet  MATH  Google Scholar 

  7. Duren, P. L., Romberg, B. W. &Shields, A. L., Linear functionals onH p spaces with 0<p<1.J. Reine Angew. Math., 238 (1969), 32–60.

    MathSciNet  MATH  Google Scholar 

  8. Eymard, P., AlgèbresA p et convoluteurs deL p. Sém. Bourbaki, 367, 1969/70.

  9. Fefferman, C. L., Inequalities for strongly singular convolution operators.Acta Math., 124 (1970), 9–36.

    MATH  MathSciNet  Google Scholar 

  10. —, Characterizations of bounded mean oscillation.Bull. Amer. Math. Soc., 77 (1971), 587–588.

    Article  MATH  MathSciNet  Google Scholar 

  11. Fefferman, C. L., to appear.

  12. Flett, T. M., On the rate of growth of mean values of holomorphic and harmonic functions.Proc. London Math. Soc. 20 (1970), 748–768.

    Google Scholar 

  13. Hardy, G. H. &Littlewood, J. E., Some properties of conjugate functions.J. Reine Angew. Math., 167 (1932), 405–423.

    MATH  Google Scholar 

  14. John, F. &Nirenberg, L., On functions of bounded mean oscillation.Comm. Pure Appl. Math., 14 (1961), 415–426.

    MathSciNet  MATH  Google Scholar 

  15. Hirschman, I. I., Jr., Multiplier transformations I.Duke Math. J., 26 (1956), 222–242.

    MathSciNet  Google Scholar 

  16. Hörmander, L.,L p estimates for (pluri-)subharmonic functions.Math. Scand., 20 (1967), 65–78.

    MATH  MathSciNet  Google Scholar 

  17. Segovia, C., On the area function of Lusin.Studia Math., 33 (1969), 312–343.

    MathSciNet  Google Scholar 

  18. Spanne, S., Sur l'interpolation entre les espacesL k .Ann. Scuola Norm. Sup. Pisa, 20 (1966), 625–648.

    MATH  MathSciNet  Google Scholar 

  19. Stein, E. M., A maximal function with applications to Fourier series.Ann. of Math., 68 (1958), 584–603.

    Article  MATH  MathSciNet  Google Scholar 

  20. —, On the functions of Littlewood-Paley, Lusin and Marcinkiewicz.Trans. Amer. Math. Soc., 88 (1958), 430–466.

    Article  MathSciNet  Google Scholar 

  21. —, Singular integrals, harmonic functions and differentiability properties of functions of several variables.Proc. Symp. in Pure Math., 10 (1967), 316–335.

    MATH  Google Scholar 

  22. Stein, E. M.,Singular integrals and differentiability properties of functions. Princeton, 1970.

  23. —,L p boundedness of certain convolution operators.Bull. Amer. Math. Soc., 77 (1971), 404–405.

    MATH  MathSciNet  Google Scholar 

  24. Stein, E. M. &Weiss, G., On the interpolation of analytic families of operators acting onH p spaces.Tôhoku Math. J., 9 (1957), 318–339.

    MathSciNet  MATH  Google Scholar 

  25. —, On the theory of harmonic functions of several variables I. The theory ofH p spaces.Acta Math., 103 (1960), 25–62.

    MathSciNet  MATH  Google Scholar 

  26. Stein, E. M. & Weiss, G.,Introduction to Fourier analysis on Euclidean spaces. Princeton, 1971.

  27. —, Generalization of the Cauchy-Riemann equations and representations of the rotation group.Amer. J. Math., 90 (1968), 163–196.

    MathSciNet  MATH  Google Scholar 

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

  29. Zygmund, A.,Trigonometric series. Cambridge, 1959.

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Fefferman, C., Stein, E.M. H p spaces of several variables. Acta Math. 129, 137–193 (1972). https://doi.org/10.1007/BF02392215

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  • DOI: https://doi.org/10.1007/BF02392215

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