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 


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Copyright information

© Hebrew University 1972

Authors and Affiliations

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

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