Skip to main content
SpringerLink
Log in

Some estimates of derivatives of rational functions in integral metrics

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

Estimates are established in the metric of Lq[0<q<p/(p+1), 0<p≤∞] of derivatives of a rational function in terms of the norm of the function itself in the metric of Lp. Local norms in Lp are also estimated of Taylor remainders of a rational function in terms of its norm in Lp.

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

Literature cited

  1. E. P. Dolzhenko, “Estimates of derivatives of rational functions,” Izv. Akad. Nauk SSSR, Ser. Matem.,27, No. 1, 9–28 (1963).

    Google Scholar 

  2. E. P. Dolzhenko, “Rational approximations and boundary properties of analytic functions,” Matem. Sb.,69, No. 4, 497–524 (1966).

    Google Scholar 

  3. A. J. MacIntyre and W. H. J. Fuchs, “Inequalities for the logarithmic derivatives of a polynomial,” J. London Math. Soc.,15, No. 1, 162–168 (1940).

    Google Scholar 

  4. A. A. Gonchar, “Inverse theorems on best approximations of rational functions,” Izv. Akad. Nauk SSSR, Ser. Matem.,25, 347–356 (1961).

    Google Scholar 

  5. E. P. Dolzhenko, “On properties of functions of several variables, sufficiently well approximated by rational fractions,” Izv. Akad. Nauk SSSR, Ser. Matem.,26, No. 5, 641–652 (1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    E. A. Sevast'yanov

Authors
  1. E. A. Sevast'yanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 13, No. 4, pp. 499–510, April, 1973.

In conclusion, the author expresses thanks to E. P. Dolzhenko, under whose guidance this work was done.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sevast'yanov, E.A. Some estimates of derivatives of rational functions in integral metrics. Mathematical Notes of the Academy of Sciences of the USSR 13, 303–309 (1973). https://doi.org/10.1007/BF01146563

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01146563

Keywords

Search

Navigation