Duke Mathematical Journal

Singular integral characterizations of Hardy spaces on homogeneous groups

Michael Christ and Daryl Geller

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 51, Number 3 (1984), 547-598.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077303949

Mathematical Reviews number (MathSciNet)
MR757953

Zentralblatt MATH identifier
0601.43003

Digital Object Identifier
doi:10.1215/S0012-7094-84-05127-5

Subjects
Primary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Secondary: 42B30: $H^p$-spaces 46E99: None of the above, but in this section 47B38: Operators on function spaces (general)

Citation

Christ, Michael; Geller, Daryl. Singular integral characterizations of Hardy spaces on homogeneous groups. Duke Math. J. 51 (1984), no. 3, 547--598. doi:10.1215/S0012-7094-84-05127-5. http://projecteuclid.org/euclid.dmj/1077303949.


Export citation

References

  • [1] L. Carleson, Two remarks on $H\sp1$ and BMO, Advances in Math. 22 (1976), no. 3, 269–277.
  • [2] S. Y. A. Chang and R. Fefferman, A continuous version of duality of $H\sp1$ with BMO on the bidisc, Ann. of Math. (2) 112 (1980), no. 1, 179–201.
  • [3] M. Christ, Characterization of $H\sp1$ by singular integrals: Necessary conditions, Duke Math. J. 51 (1984), no. 3, 599–609.
  • [4] R. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.
  • [5] C. Fefferman and E. M. Stein, $H\spp$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193.
  • [6] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), no. 2, 161–207.
  • [7] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Mathematical Notes, vol. 28, Princeton University Press, Princeton, N.J., 1982.
  • [8] D. Geller, Fourier analysis on the Heisenberg group. I. Schwartz space, J. Funct. Anal. 36 (1980), no. 2, 205–254.
  • [9] D. Geller, Local solvability and homogeneous distributions on the Heisenberg group, Comm. Partial Differential Equations 5 (1980), no. 5, 475–560.
  • [10] D. Geller, Some results in $H\spp$ theory for the Heisenberg Group, Duke Math. J. 47 (1980), no. 2, 365–390.
  • [11] D. Geller, Spherical harmonics, the Weyl transform and the Fourier transform on the Heisenberg group, to appear in Canad. J. Math.
  • [12] A. Grossman, G. Loupias, and E. M. Stein, An algebra of pseudodifferential operators and quantum mechanics in phase space, Ann. Inst. Fourier Grenoble 18 (1968), 343–368.
  • [13] B. Helffer and J. Nourrigat, Caracterisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe de Lie nilpotent gradué, Comm. Partial Differential Equations 4 (1979), no. 8, 899–958.
  • [14] B. Helffer and F. Nourrigat, Hypoellipticité pour des groupes nilpotents de rang de nilpotence $3$, Comm. Partial Differential Equations 3 (1978), no. 8, 643–743.
  • [15] S. Janson, Characterizations of $H\sp1$ by singular integral transforms on martingales and $\bf R\spn$, Math. Scand. 41 (1977), no. 1, 140–152.
  • [16] A. Koranyi, Harmonic functions on Hermitian hyperbolic space, Trans. Amer. Math. Soc. 135 (1969), 507–516.
  • [17] M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1975.
  • [18] L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320.
  • [19] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970.
  • [20] E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables. I. The theory of $H\spp$-spaces, Acta Math. 103 (1960), 25–62.
  • [21] M. Taylor, The Heisenberg group, preprint.
  • [22] F. Trèves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.
  • [23] A. Uchiyama, A constructive proof of the Fefferman-Stein decomposition of BMO $(\bf R\spn)$, Acta Math. 148 (1982), 215–241.
  • [24] A. Uchiyama, The Fefferman–Stein decomposition of smooth functions and its application to $H^p(\mathsfR^n)$, Ph.D. thesis, University of Chicago, June 1982.