Israel Journal of Mathematics

, Volume 12, Issue 2, pp 184–189 | Cite as

Estimates of ‖e itf A(Γ), when Γ ⊂ ℝ n is a curve andf is a real-valued functionis a curve andf is a real-valued function

  • Yngve Domar


Γ is a simple curve in ℝ n with an equationx=γ(u),u∈[0. 1], γ∈C k, where for somek, 2≦k−1≦n, γ′(u), γ″(u),…,γ k−1(u) are linearly independent for everyu. It is then proved that if t ∈ ℝ and f is a real-valued function in C k(Γ),t −1/ke itf A(Γ) is bounded as |t|→∞. An example shows that the estimate cannot be improved in general, whenn=2,k=3. The result is interpreted in terms of properties of the space of pseudomeasures on Γ.


Springer Lecture Note Simple Curve Adjoint Mapping Closed Graph Theorem Full Discus 
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.
    A. Beurling,Sur les intégrales de Fourier absolumentes convergentes et leur application à une transformation fonctionelle, Neuvième congrès des mathématiciens scandinaves, Helsinki, 1938.Google Scholar
  2. 2.
    F. Carlson,Une inégalité, Ark. Mat. Astronom. Fys., 25, B1, 1934.CrossRefGoogle Scholar
  3. 3.
    Y. Domar, Sur la synthèse harmonique des courbes de ℝ2, C. R. Acad. Sci. Paris270 (1970), 875–878.MATHMathSciNetGoogle Scholar
  4. 4.
    Z. L. Leibenson,On the ring of functions with absolutely convergent Fourier series, Uspehi Matem. Nauk. (N.S.)9 (61) (1954), 157–162.Google Scholar
  5. 5.
    H. S. Shapiro,Topics in approximation theory, Springer Lecture Notes 187, 1971.Google Scholar

Copyright information

© Hebrew University 1972

Authors and Affiliations

  • Yngve Domar
    • 1
  1. 1.University of UppsalaSweden

Personalised recommendations