Ukrainian Mathematical Journal

, Volume 64, Issue 5, pp 693–710 | Cite as

Fourier cosine and sine transforms and generalized Lipschitz classes in the uniform metric

  • B. I. Golubov
  • S. S. Volosivets

For functions fL 1 (ℝ+) with cosine (sine) Fourier transforms \( {{\hat{f}}_c} \) \( \left( {{{\hat{f}}_s}} \right) \) in L 1 (ℝ), we give necessary and sufficient conditions in terms of \( {{\hat{f}}_c} \) \( \left( {{{\hat{f}}_s}} \right) \) for f to belong to generalized Lipschitz classes H ω,m and h ω,m Conditions for the uniform convergence of the Fourier integral and for the existence of the Schwartz derivative are also obtained.


Fourier Series Inversion Formula Trigonometric Series Similar Assertion FOURIER Cosine 
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • B. I. Golubov
    • 1
  • S. S. Volosivets
    • 2
  1. 1.Moscow Institute of Physics and Technology (State University)MoscowRussia
  2. 2.Saratov State UniversitySaratovRussia

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