Duke Mathematical Journal

Distribution function estimates for Marcinkiewicz integrals and differentiability

Sagun Chanillo and Richard L. Wheeden

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Duke Math. J., Volume 49, Number 3 (1982), 517-619.

First available in Project Euclid: 20 February 2004

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Primary: 42B25: Maximal functions, Littlewood-Paley theory


Chanillo, Sagun; Wheeden, Richard L. Distribution function estimates for Marcinkiewicz integrals and differentiability. Duke Math. J. 49 (1982), no. 3, 517--619. doi:10.1215/S0012-7094-82-04930-4. https://projecteuclid.org/euclid.dmj/1077315379

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  • [1] D. L. Burkholder, R. F. Gundy, and M. L. Silverstein, A maximal function characterization of the class $H\spp$, Trans. Amer. Math. Soc. 157 (1971), 137–153.
  • [2] D. L. Burkholder and R. F. Gundy, Distribution function inequalities for the area integral, Studia Math. 44 (1972), 527–544.
  • [3] A.-P. Calderón and A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171–225.
  • [4] A. P. Calderón, Estimates for singular integral operators in terms of maximal functions, Studia Math. 44 (1972), 563–582.
  • [5] R. DeVore and R. Sharpley, Maximal functions measuring smoothness, to appear.
  • [6] C. L. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36.
  • [7] A. B. E. Gatto, J. R. Jiménez, and C. Segovia, On the solutions of the equation $\Delta^mF=f$ for $f\in H^p$, to appear in Conference on Harmonic Analysis in Honor of Antoni Zygmund, Wadsworth International, California, 1982.
  • [8] I. I. Hirschman, Jr., Fractional integration, Amer. J. Math. 75 (1953), 531–546.
  • [9] J. Marcinkiewicz, Sur quelques intégrals du type de Dini, Ann. Soc. Polonaise Math. 17 (1938), 42–50.
  • [10] C. Segovia and R. L. Wheeden, On certain fractional area integrals, J. Math. Mech. 19 (1969/1970), 247–262.
  • [11] E. M. Stein and A. Zygmund, On the differentiability of functions, Studia Math. 23 (1963/1964), 247–283.
  • [12] E. M. Stein and A. Zygmund, On the fractional differentiability of functions, Proc. London Math. Soc. (3) 14a (1965), 249–264.
  • [13] E. M. Stein, The characterization of functions arising as potentials, Bull. Amer. Math. Soc. 67 (1961), 102–104.
  • [14] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970.
  • [15] D. Waterman, On an integral of Marcinkiewicz, Trans. Amer. Math. Soc. 91 (1959), 129–138.
  • [16] G. Weiss, lecture notes.
  • [17] R. L. Wheeden, On the $n$-dimensional integral of Marcinkiewicz, J. Math. Mech. 14 (1965), 61–70.
  • [18] A. Zygmund, A theorem on generalized derivatives, Bull. Amer. Math. Soc. 49 (1943), 917–923.
  • [19] A. Zygmund, On certain integrals, Trans. Amer. Math. Soc. 55 (1944), 170–204.