Some Singular Integrals on the Affine Group

  • G. I. Gaudry
Conference paper


The affine group of the plane is usually thought of as the set {(b, a): a ∈ R+, b ∈ R} with the composition law (b, a)(d, c) = (b + ad, ac). For the sake of convenience, we realise it as G = {(s, t): s, t ∈ R}, with group product (u, v)(s, t) = (u + e v s, v + t).


Singular Integral Weak Type Local Part Abelian Normal Subgroup Affine Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. J. Burns and D. W. Robinson, A ‘priori inequalities on Lie groups. Preprint.Google Scholar
  2. [2]
    G. I. Gaudry, P. Sjogren, T. Qian, Singular integrals associated to the Laplacian on the affine group ax + b. Submitted.Google Scholar
  3. [3]
    A. Hulanicki, On the spectrum of the Laplacian on the affine group of the real line. Studia Math. LIV (1976), 199 - 204.Google Scholar
  4. [4]
    T. Kato, “Perturbation theory for linear operators”. Springer-Verlag, Berlin- Heidelberg -New York 1966.MATHGoogle Scholar
  5. [5]
    W. Magnus, F. Oberhettinger, R. P. Soni, “Formulas and Theorems for the Special Functions of Mathematical Physics”. Springer-Verlag, Berlin-Heidelberg-New York 1966.MATHGoogle Scholar
  6. [6]
    E. M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory. Annals of Math. Studies, No. 63. Princeton University Press. Princeton, NJ 1970.Google Scholar
  7. [7]
    R. S. Strichartz, Analysis of the Laplacian on a complete Riemannian manifold. J. Funct. Anal. 52 (1983), 48 - 79.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    H. Tanabe, “Equations of Evolution”. Pitman, London-San Francisco-Melbourne 1979.MATHGoogle Scholar
  9. [9]
    K. Yosida, “Functional Analysis”. Second Edition. Springer-Verlag, Berlin-Heidelberg -New York 1968.Google Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • G. I. Gaudry
    • 1
  1. 1.Mathematics DisciplineFlinders UniversityAdelaideAustralia

Personalised recommendations