Mathematical Notes

, Volume 64, Issue 5, pp 616–621 | Cite as

Embeddings of the classesHω

  • M. V. Medvedeva
Article

Abstract

In this paper we study functions belonging to the classesVε and ΛBV, which are encountered in the theory of Fourier trigonometric series. Necessary and sufficient conditions for the embedding of the classesHω in the classesVϕ and ABV are obtained.

Key words

Fourier series Hω-class Vϕ--class ΛBV-class embedding of the classesHω modulus of continuity function of Λ-bounded variation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. C. Young, “General inequalities for Stieltjes integrals and the convergence of Fourier series,”Math. Ann.,115, No. 4, 581–612 (1938).MATHMathSciNetGoogle Scholar
  2. 2.
    A. A. Saakyan, “On convergence of double Fourier series of functions of bounded harmonic variation,”Izv. Akad. Azerbaidzhan. SSR Ser. Mat., No. 6, 517–529 (1987).Google Scholar
  3. 3.
    D. Waterman, “On convergence of Fourier series of functions of generalized bounded variation,”Stadia. Math.,44, No. 2, 107–117 (1972).MATHMathSciNetGoogle Scholar
  4. 4.
    G. H. Hardy and J. E. Littlewood, “A convergence criterion for Fourier series,”Math. Z.,28, No. 4, 612–634 (1928).MathSciNetGoogle Scholar
  5. 5.
    P. L. Ul'yanov, “Embedding of some function classesH pω,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. VSSR-Izv.],32, No. 3, 649–686 (1968).MATHMathSciNetGoogle Scholar
  6. 6.
    O. Kovacik, “On the embeddingH wV p,”Math. Shovaca,43, No. 5, 573–578 (1993).MATHMathSciNetGoogle Scholar
  7. 7.
    N. P. Korneichuk,Extremum Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • M. V. Medvedeva
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

Personalised recommendations