Skip to main content
SpringerLink
Log in

On a multidimensional version of the Hilbert type inequality

Об одном многомерном варианте неравенства типа Гильберта

  • Published:
Analysis Mathematica Aims and scope Submit manuscript

Abstract

The main objective of this paper is a study of some new multidimensional Hilbert type inequalities with a general homogeneous kernel. We derive a pair of equivalent inequalities, and also establish the conditions under which the constant factors included in the obtained inequalities are the best possible. Some applications in particular settings are also considered.

Реэюме

Основной целью работы является изучение новых многомерных неравенств типа Гильберта с общим однородным ядром. Получены пары эквивалентных неравенств и выяснены условия, при которых постоянные в этих соотношениях наилучшие. Рассмотрены и некоторые приложения общих результатов в конкретных частных случаях.

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. Y. Bicheng, I. Brnetić, M. Krnić, and J. Pečarić, Generalization of Hilbert and Hardy-Hilbert integral inequalities, Math. Inequal. Appl. 8(2005), 259–272.

    MathSciNet  MATH  Google Scholar 

  2. Y. Bicheng and M. Krnić, On the norm of multidimensional Hilbert type operator, Sarajevo J. Math., 7(2011), 2.23–243.

    Google Scholar 

  3. G. M. Fihtengolz, A course in differential and integral calculus, Izd-vo Nauka (Moskva, 1966) (in Russian).

    Google Scholar 

  4. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd edition, Cambridge University Press (Cambridge, 1967).

    Google Scholar 

  5. D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers (Dordrecht-Boston-London, 1993).

    MATH  Google Scholar 

  6. T. M. Rassias and B. Yang, On the way of weight coefficient and research for the Hilbert type inequalities, Math. Inequal. Appl., 6(2003), 625–658.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering and Computing, Unska 3, 10000, Zagreb, Croatia

    Mario Krnić

  2. Faculty of Teacher Education, University of Zagreb, Ante Starčevića 55, 40000, Čakovec, Croatia

    Predrag Vuković

Authors
  1. Mario Krnić
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Predrag Vuković
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Krnić.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krnić, M., Vuković, P. On a multidimensional version of the Hilbert type inequality. Anal Math 38, 291–303 (2012). https://doi.org/10.1007/s10476-012-0402-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10476-012-0402-2

Keywords

Search

Navigation