Skip to main content

On the mean summability by Cesaro method of Fourier trigonometric series in two-weighted setting

Abstract

The Cesaro summability of trigonometric Fourier series is investigated in the weighted Lebesgue spaces in a two-weight case, for one and two dimensions. These results are applied to the prove of two-weighted Bernstein's inequalities for trigonometric polynomials of one and two variables.

[123456789]

References

  1. 1.

    Banach S, Steinhaus H: Sur le principe de condensation de singularités. Fundamenta Mathematicae 1927, 9: 50–61.

    MATH  Google Scholar 

  2. 2.

    Kokilashvili V, Krbec M: Weighted Inequalities in Lorentz and Orlicz Spaces. World Scientific, New Jersey; 1991:xii+233.

    Google Scholar 

  3. 3.

    Muckenhoupt B: Weighted norm inequalities for the Hardy maximal function. Transactions of the American Mathematical Society 1972, 165: 207–226.

    MATH  MathSciNet  Article  Google Scholar 

  4. 4.

    Muckenhoupt B: Two weight function norm inequalities for the Poisson integral. Transactions of the American Mathematical Society 1975, 210: 225–231.

    MATH  MathSciNet  Article  Google Scholar 

  5. 5.

    Nakhman AD, Osilenker BP: Estimates of weighted norms of some operators generated by multiple trigonometric Fourier series. Izvestiya Vysshikh Uchebnykh Zavedeniĭ. Matematika 1982,239(4):39–50.

    MathSciNet  Google Scholar 

  6. 6.

    Rosenblum M: Summability of Fourier series in. Transactions of the American Mathematical Society 1962,105(1):32–42.

    MATH  MathSciNet  Google Scholar 

  7. 7.

    Tsanava Ts: On the Fourier operators in weighted Lebesgue spaces. Proceedings of A. Razmadze Mathematical Institute 2005, 138: 107–109.

    Google Scholar 

  8. 8.

    Žižiašvili LV: Conjugate Functions and Trigonometric Series. Izdat. Tbilis. Univ., Tbilisi; 1969:271.

    Google Scholar 

  9. 9.

    Zygmund A: Trigonometric Series. Vols. I, II. 2nd edition. Cambridge University Press, New York; 1959:Vol. I. xii+383; Vol. II. vii+354.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. Guven.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Guven, A., Kokilashvili, V. On the mean summability by Cesaro method of Fourier trigonometric series in two-weighted setting. J Inequal Appl 2006, 41837 (2006). https://doi.org/10.1155/JIA/2006/41837

Download citation

Keywords

  • Fourier Series
  • Trigonometric Polynomial
  • Lebesgue Space
  • Trigonometric Series
  • Weighted Lebesgue Space
\