Pacific Journal of Mathematics

The Fefferman-Stein decomposition of smooth functions and its application to $H^{p}({\bf R}^{n})$.

Akihito Uchiyama

Article information

Source
Pacific J. Math., Volume 115, Number 1 (1984), 217-255.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102708422

Mathematical Reviews number (MathSciNet)
MR762212

Zentralblatt MATH identifier
0562.42019

Subjects
Primary: 42B30: $H^p$-spaces
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

Citation

Uchiyama, Akihito. The Fefferman-Stein decomposition of smooth functions and its application to $H^{p}({\bf R}^{n})$. Pacific J. Math. 115 (1984), no. 1, 217--255. https://projecteuclid.org/euclid.pjm/1102708422


Export citation

References

  • [I] A. P. Caldern, An atomic decomposition of distributions in parabolic Hp spaces, Advances in Math.,25 (1977), 216-225.
  • [2] A. P. Caldern and A. Zygmund, On higher gradients of harmonic functions, Studia Math., 24 (1964), 211-226.
  • [3] L. Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math.,76 (1962), 547-559.
  • [4] L. Carleson, The Corona Theorem, Proceedings of 15th Scandinavian Congress (Oslo, 1968), Springer-Verlag Lecture Notes in Math.,No. 118, 121-132.
  • [5] L. Carleson, Two remarks on Hx and BMO, Advances in Math.,22 (1976), 269-277.
  • [6] L. Carleson,An explicit unconditional basis in H\ Bull. Sci. Math., 104 (1980), 405-416.
  • [7] S-Y. A. Chang and R. Fefferman, A continuous version of duality of Hx and BMO on the bidisc, Ann. of Math., 112 (1980), 179-201.
  • [8] R. Coifman and B. Dahlberg, Singular integral characterization of nonisotropic Hp spaces and the F. and M. Riesz theorem, Proc. Symp. Pure Math., 35 (1979), 231-234.
  • [9] R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc, 79 (1980), 249-254.
  • [10] R. Coifman and G. Weiss, On subharmonicity inequalities involving solutions of generalized Cauchy-Riemann equations, Studia Math.,36 (1970), 77-83.
  • [II] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc, 83(1977), 569-646.
  • [12] O. D. Csereteli, On conjugatefunctions, Mat. Zametki, 22 (1977), 771-781.
  • [13] C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc, 77(1971), 587-588.
  • [14] C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Math., 129 (1972), 137-193.
  • [15] A. Gandulfo, J. Garcia-Cuerva and M. Taibleson, Conjugate system characterization of H; counter examples for the Euclidean plane and local fields, Bull. Amer. Math. Soc, 82 (1976), 83-85.
  • [16] J. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
  • [17] J. Garnett and P. Jones, The distance in BMO to L, Ann. of Math., 108 (1978), 373-393.
  • [18] R. F. Gundy, On a theorem of F. and M. Riesz and an equation of A. Wald, Indiana Univ. Math.J., 30 (1981), 589-605.
  • [19] L. Hrmander, Lp estimates for (pluri-) subharmonic functions, Math. Scand., 20 (1967), 65-78.
  • [20] S. Janson, Characterization of H] by singular integral transforms on martingales and Rn, Math. Scand., 41 (1977), 140-152.
  • [21] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14 (1961), 415-426.
  • [22] P. Jones, Constructions with functions of bounded mean oscillation, Ph.D. Thesis, University of California, 1978.
  • [23] P. Jones, Carleson measures and the Fefferman-Stein decomposition of BMO(R), Ann. of Math., Ill (1980), 197-208.
  • [24] P. Jones, Factorization of Ap weights, Ann. of Math., Ill (1980), 511-530.
  • [25] P. Jones, L estimates for the problem in a half-plane, to appear in Acta Math.
  • [26] B. Muckenhoupt and R. Wheeden, Weighted bounded mean oscillation and the Hubert transform, Studia Math., 54 (1976), 221-237.
  • [27] B. Muckenhoupt and R. Wheeden, On the dual of weighted H of the half-space, Studia Math., 63 (1978), 57-79.
  • [28] J. Peetre, On Littlewood's conjecture and Hardy's inequality, A connection with a problem in interpolation spaces, preprint.
  • [29] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, New Jersey, 1970.
  • [30] E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables I, The theory of Hp spaces, Acta Math., 103 (1960), 26-62.
  • [31] A. Uchiyama, A constructive proof of the Fefferman-Stein decomposition of BMO on simple martingales, to appear in the Proceedings of the conference in honor of Antoni Zygmund, held at the University of Chicago, 1981.
  • [32] A. Uchiyama, A constructive proof of the Fefferman-Stein decomposition of BM0(R"), Acta Math., 148 (1982), 215-241.
  • [33] N. Th. Varopoulos,BMO functions and the equation, Pacific J. Math., 71 (1977), 221-273.
  • [34] N. Th. Varopoulos, A theorem of weak type estimates for Riesz transforms and martingale transforms, Ann. Inst. Fourier, 31 (1981), 257-264.
  • [35] G. Weiss, Some problems in the theory of Hardy spaces, Proc. Symp. Pure Math., 35 (1979), 189-200.