Skip to main content
SpringerLink
Log in

On the classes H p ω and Lip (α, p) for trigonometric series with monotone coefficients

  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

The paper is devoted to the study of a relationship between the behavior of the coefficients of trigonometric series of many variables and the smoothness of the sums of these series in the spaces L p .

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Zygmund, Trigonometric Series. Vol. 2 (Cambridge University Press, Cambridge–New York, 1988; transl. of the 1st ed., Mir, Moscow, 1965).

    MATH  Google Scholar 

  2. F. Moricz, “On Double Cosine, Sine and Walsh Series with Monotone Coefficients,” Proc. Amer. Math. Soc. 109 (2), 417–435 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  3. M. I. D’yachenko, “Norms of Dirichlet kernels and of some other trigonometric polynomials in Lp spaces,” Mat. Sb. 184 (3), 3–20 (1993) [Russian Acad. Sci. Sb. Math. 78 (2), 267–282 (1994)].

    MATH  Google Scholar 

  4. O. S. Dragoshanskii, “Anisotropic norms of Dirichlet kernels and of some other trigonometric polynomials,” Mat. Zametki 67 (5), 686–701 (2000) [Math. Notes 67 (5–6), 582–595 (2000)].

    Article  MathSciNet  Google Scholar 

  5. G. G. Lorentz, “Fourier–Koeffizienten und Funktionenklassen,” Math. Z. 51 (2), 135–149 (1948).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. A. Konyushkov, “On Lipschitz classes,” Izv. Akad. Nauk SSSR. Ser. Mat. 21, 423–448 (1957).

    MathSciNet  Google Scholar 

  7. T. Sh. Tevzadze, “Some classes of functions and trigonometric Fourier series,” Soobshch. Akad. Nauk Gruzin. SSR 105 (2), 253–256 (1982).

    MathSciNet  MATH  Google Scholar 

  8. T. M. Vukolova and M. I. D’yachenko, “Estimates for the norms of sums of double trigonometric series with multiply monotone coefficients,” Izv. Vyssh. Uchebn. Zaved. Mat. (7), 20–28 (1994) [Russian Math. (Iz. VUZ) 38 (7), 18–26 (1994)].

    MathSciNet  MATH  Google Scholar 

  9. A. F. Timan, Theory of Approximation of Functions of a Real Variable (Fizmatgiz, Moscow, 1960; Dover Publications, Inc., New York, 1994).

    Google Scholar 

  10. S. M. Nikol’skii, Approximation of Functions of Several Variables and Imbedding Theorems (Nauka, Moscow, 1977; Springer-Verlag, New York–Heidelberg. 1975).

    MATH  Google Scholar 

  11. M. I. D’jachenko, “Multiple Trigonometric Series with Lexicographically Monotone Coefficients,” Analysis Math. (16), (3), 173–190 (1990).

    Article  MathSciNet  Google Scholar 

  12. A. P. Antonov, “Smoothness of Sums of Double Trigonometric Series with Monotone Coefficients,” Vestnik Moskov. Univ. Ser. I Mat. Mekh. (5), 26–33 (2004) [Moscow Univ. Math. Bull. 59 (5), 27–35 (2004) (2005)].

    MathSciNet  MATH  Google Scholar 

  13. A. P. Antonov, “On Nikol’skii Classes for Double Trigonometric Series with Monotone Coefficients,” Russ. J. Math. Phys. 21 (2), 148–155 (2014).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. P. Antonov

Authors
  1. A. P. Antonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. P. Antonov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Antonov, A.P. On the classes H p ω and Lip (α, p) for trigonometric series with monotone coefficients. Russ. J. Math. Phys. 23, 335–342 (2016). https://doi.org/10.1134/S1061920816030031

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920816030031

Search

Navigation