Pacific Journal of Mathematics

Extension of the Hardy-Littlewood-Fefferman-Stein inequality.

Akihito Uchiyama

Article information

Source
Pacific J. Math., Volume 120, Number 1 (1985), 229-255.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102703896

Mathematical Reviews number (MathSciNet)
MR808940

Zentralblatt MATH identifier
0583.42009

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B30: $H^p$-spaces 46E99: None of the above, but in this section

Citation

Uchiyama, Akihito. Extension of the Hardy-Littlewood-Fefferman-Stein inequality. Pacific J. Math. 120 (1985), no. 1, 229--255. https://projecteuclid.org/euclid.pjm/1102703896


Export citation

References

  • [1] A. Caldern andA. Torchinsky, Parabolic maximal functions associated with a distribution, Advances in Math., 16 (1975), 1-63.
  • [2] R. Coifman andG.Weiss, Extensions of Hardy spaces and their useinanalysis, Bull. Amer. Math. Soc, 83(1977), 569-646.
  • [3] P. Duren, Extension of a theorem of Carleson, Bull. Amer. Math. Soc, 75 (1969), 143-146.
  • [4] C. Feffenan, N. Riviere and Y. Sagher, Interpolation between Hp spaces, the real method,Trans. Amer. Math. Soc, 191 (1974), 75-81.
  • [5] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math.,93 (1971), 107-115.
  • [6] C. Fefferman and E. M. Stein, Hp spacesof severalvariables, Acta Math., 129 (1972), 137-193.
  • [7] R. Fefferman and E. M. Stein, Singular integrals on product spaces, Advances in Math., 45 (1982), 117-143.
  • [8] G. H. Hardy and L. E. Littlewood, Some properties of conjugatefunctions, J. fur Mathematick, 167 (1932), 405-423.
  • [9] E. M. Stein, Singular Integrals and Differentiability Properties of Functions,Princeton, 1970.
  • [10] M. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Asterisque, 77 (1980), 67-149.
  • [11] A. Torchinsky, On a mean value inequality, Bull. Amer. Math. Soc, 81 (1975), 950-953.
  • [12] A. Uchiyama, A maximal function characterization of Hp on the space of homogeneous type, Trans. Amer. Math. Soc, 262 (1980), 579-592.
  • [13] A. Uchiyama, Grand maximalfunctions and radial maximalfunctions,preprint.
  • [14] A. Uchiyama, Characterization of Hp(Rn)in terms of generalized Littlewood-Paley g-func- tions, to appear in Studia Math.