Skip to main content

Advertisement

Log in

Marchaud’s Inequality for Multiple Modules of Continuity in Metric Spaces

  • BRIEF COMMUNICATIONS
  • Published:
Ukrainian Mathematical Journal Aims and scope

For periodic functions of one variable in the metric spaces LΨ [0, 2π], we establish an analog of Marchaud’s inequality for multiple modules of continuity.

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

Access this article

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

Instant access to the full article PDF.

References

  1. A. Marchaud, “Sur les dérivées et sur les différences des fonctions de variables réeles,” J. Math. Pures Appl., 6, 337–425 (1927).

    MATH  Google Scholar 

  2. M. F. Timan, Specific Features of the Main Theorems of the Constructive Theory of Functions in the Spaces Lpand Some Applications [in Russian], Author’s Abstract of the Doctoral-Degree Thesis (Physics and Mathematics), Tbilisi (1962).

  3. M. F. Timan, Approximation and Properties of Periodic Functions [in Russian], Poligrafist, Dnepropetrovsk (2000).

  4. S. G. Krein, Yu. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators [in Russian], Nauka, Moscow (1978).

  5. S. A. Pichugov, “Multiple modules of continuity and the best approximations of periodic functions in metric spaces,” Ukr. Mat. Zh., 70, No. 5, 699–707 (2018); English translation:Ukr. Math. J., 70, No. 5, 806–818 (2018).

  6. S. A. Pichugov, “Inverse Jackson theorems in spaces with integral metric,” Ukr. Mat. Zh., 64, No. 3, 351–362 (2012); English translation:Ukr. Math. J., 64, No. 3, 394–407 (2012).

  7. V. I. Ivanov, “Direct and inverse theorems of the approximation theory in the metric of Lp for 0 < p < 1,Mat. Zametki, 18, No. 5, 641–658 (1975).

    MathSciNet  Google Scholar 

  8. É. A. Storozhenko, V. G. Krotov, and P. Oswald, “Direct and inverse Jackson-type theorems in the spaces Lp, 0 < p < 1,Mat. Sb., 98, No. 3, 395–415 (1975).

    MathSciNet  Google Scholar 

  9. É. A. Storozhenko and P. Oswald, “Jackson theorem in the spaces Lp(Rk), 0 < p < 1,Sib. Mat. Zh., 19, No. 4, 888–901 (1978).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. A. Pichugov.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 12, pp. 1712–1716, December, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pichugov, S.A. Marchaud’s Inequality for Multiple Modules of Continuity in Metric Spaces. Ukr Math J 71, 1959–1964 (2020). https://doi.org/10.1007/s11253-020-01758-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-020-01758-1

Navigation