Analysis Mathematica

, Volume 38, Issue 4, pp 291–303 | Cite as

On a multidimensional version of the Hilbert type inequality



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.

Об одном многомерном варианте неравенства типа Гильберта


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.


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  1. [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.MathSciNetMATHGoogle Scholar
  2. [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. [3]
    G. M. Fihtengolz, A course in differential and integral calculus, Izd-vo Nauka (Moskva, 1966) (in Russian).Google Scholar
  4. [4]
    G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd edition, Cambridge University Press (Cambridge, 1967).Google Scholar
  5. [5]
    D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers (Dordrecht-Boston-London, 1993).MATHGoogle Scholar
  6. [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.MathSciNetMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering and ComputingZagrebCroatia
  2. 2.Faculty of Teacher EducationUniversity of ZagrebČakovecCroatia

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