Skip to main content
SpringerLink
Log in

Estimates of norms of functions represented as double series over cosines with multiple-monotone coefficients

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

Lower and upper bounds are proved for the norms of functions being sums of double series in cosines.

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. G. H. Hardy, “On Double Fourier Series and Especially those which Represent the Double Zeta Functions with Real and Incommensurable Parameters,” Quart. J. Math. 37 (1). 53 (1906).

    MATH  Google Scholar 

  2. T. M. Vukolova and M. I. D’yachenko, “Estimates of Mixed Norms of Sums of Double Trigonometric Series with Multiple-Monotone Coefficients,” Izvestiya Vuzov, Matem., No. 3, 3 (1997).

    MATH  Google Scholar 

  3. T. M. Vukolova, “Properties of Functions Representable by Trigonometric Sine Series with Multiple-Monotone Coefficients,” Vestn. Mosk. Univ., Matem. Mekhan., No. 6, 61 (2007).

    MathSciNet  MATH  Google Scholar 

  4. T. M. Vukolova, “Properties of Sums of Cosine Series with Multiple-Monotone Coefficients,” in Proc. Int. Conf. “Theory of Functions and Computational Methods” dedicated to the 60th anniversary of Prof. N. Temirgaliev. Astana, June 5–9, 2007 (Astana, 2007), pp. 73–74.

    Google Scholar 

  5. T. M. Vukolova, “Estimates of Mixed Norms of Functions Representable by Double Sine Series with Multiple-Monotone Coefficients,” Vestn. Mosk. Univ., Matem. Mekhan., No. 6, 61 (2013).

    MathSciNet  MATH  Google Scholar 

  6. T. M. Vukolova, “Estimates of Mixed Norms of Functions Representable by Series over Products of Cosines and Sines with Multiple-Monotone Coefficients,” Vestn. Mosk. Univ., Matem. Mekhan., No. 5, 3 (2014).

    MathSciNet  MATH  Google Scholar 

  7. T. M. Vukolova and M. I. D’yachenko, “Properties of Sums of Trigonometric Series with Monotone Coefficients,” Vestn. Mosk. Univ., Matem. Mekhan., No. 3, 22 (1995).

    MathSciNet  MATH  Google Scholar 

  8. N. K. Bari, Trigonometric Series (Nauka, Moscow, 1961) [in Russian].

    Google Scholar 

  9. T. M. Vukolova, “Estimates of Mixed Norms of Derivatives and Mixed Moduli of Smoothness of Functions Having Monotone Fourier Coefficients,” Matem. Zametki 97 (6), 841 (2015).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Institute of Russian Language and Culture, 24/35, bldg 1 Krzhizhanovskogo st., Moscow, 117218, Russia

    T. M. Vukolova

Authors
  1. T. M. Vukolova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. M. Vukolova.

Additional information

Original Russian Text © T.M. Vukolova, 2017, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2017, Vol. 72, No. 5, pp. 3–13.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vukolova, T.M. Estimates of norms of functions represented as double series over cosines with multiple-monotone coefficients. Moscow Univ. Math. Bull. 72, 181–191 (2017). https://doi.org/10.3103/S0027132217050011

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132217050011

Search

Navigation