Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On some properties of multiple conjugate trigonometric series

  • 12 Accesses

Abstract

We have obtained an estimate, in terms of partial and mixed moduli, of the continuity of deviation of the Cesáro (C, α) means (α = (α1,...,αn),αi∈ ℝ, α1 > −1,\(i = \overline {1,n} \)) of the sequence of rectangular partial sums ofn-multiple (n>1) conjugate trigonometric series from then-multiple truncated conjugate function. This estimate implies the result on them λ-convergence (λ≥1) of (C, α) means (α1 > 0,\(i = \overline {1,n} \)) provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown that them λ-convergence cannot be replaced by ordinary convergence.

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

References

  1. 1.

    L. V. Zhizhiashvili, Conjugate functions and trigonometric series. (Russian)Tbilisi University Press, Tbilisi, 1969.

  2. 2.

    A. Zygmund, Trigonometric series, v.1. (Translated into the Russian) “Mir,”Moscow, 1965; English original:Cambridge, 1959.

  3. 3.

    G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities. (Translated into the Russian) “IL,”Moscow, 1949; English original:Cambridge, 1934.

  4. 4.

    M. M. Lekishvili, On approximation of periodic functions by (C, α) means. (Russian)Mat. Sb.,121 (163)(1983), No. 4(8), 499–509.

  5. 5.

    L. V. Zhizhiashvili, On some problems from the theory of simple and multiple trigonometric and orthogonal series. (Russian)Uspekhi Mat. Nauk 28(1973), No. 2, 65–119.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Leladze, D. On some properties of multiple conjugate trigonometric series. Georgian Mathematical Journal 1, 287–302 (1994). https://doi.org/10.1007/BF02254677

Download citation

1991 Mathematics Subject Classification

  • 42B08