Banach Journal of Mathematical Analysis

Multiple Hilbert-type inequalities involving some differential operators

Vandanjav Adiyasuren, Tserendorj Batbold, and Mario Krnić

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Abstract

In this article, we derive several multidimensional Hilbert-type inequalities, including certain differential operators. Further, we determine the conditions under which the constants appearing on the right-hand sides of the established inequalities are the best possible. As an application, some particular examples are also studied.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 2 (2016), 320-337.

Dates
Received: 6 April 2015
Accepted: 10 June 2015
First available in Project Euclid: 4 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1459772692

Digital Object Identifier
doi:10.1215/17358787-3495561

Mathematical Reviews number (MathSciNet)
MR3481107

Zentralblatt MATH identifier
1337.26027

Subjects
Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 33B15: Gamma, beta and polygamma functions

Keywords
Hilbert-type inequality Hardy inequality differential operator best constant

Citation

Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario. Multiple Hilbert-type inequalities involving some differential operators. Banach J. Math. Anal. 10 (2016), no. 2, 320--337. doi:10.1215/17358787-3495561. https://projecteuclid.org/euclid.bjma/1459772692


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References

  • [1] V. Adiyasuren, T. Batbold, and M. Krnić, On several new Hilbert-type inequalities involving means operators, Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 8, 1493–1514.
  • [2] V. Adiyasuren, T. Batbold, and M. Krnić, Hilbert-type inequalities involving differential operators, the best constants, and applications, Math. Inequal. Appl. 18 (2015), no. 1, 111–124.
  • [3] F. F. Bonsall, Inequalities with non-conjugate parameters, Quart. J. Math., Oxford Ser. (2) 2 (1951), 135–150.
  • [4] G. H. Hardy, Notes on some points in the integral calculus, LXIV, Messenger Math. 57 (1928), 12–16.
  • [5] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, Cambridge, 1967.
  • [6] M. Krnić, J. Pečarić, I. Perić, and P. Vuković, Recent Advances in Hilbert-Type Inequalities, Monogr. Inequal., Element, Zagreb, 2012.
  • [7] A. Kufner, L. Maligranda, and L. E. Persson, The Hardy Inequality: About Its History and Some Related Results, Vydavatelský Servis, Pilsen, 2007.
  • [8] I. Perić and P. Vuković, Multiple Hilbert’s type inequalities with a homogeneous kernel, Banach J. Math. Anal. 5 (2011), no. 2, 33–43.
  • [9] L. E. Persson, M. A. Ragusa, N. Samko, and P. Wall, Commutators of Hardy operators in vanishing Morrey spaces, AIP Conf. Proc. 1493 (2012), 859–866.
  • [10] P. Vuković, Note on Hilbert-type inequalities, Turkish J. Math. 36 (2012), no. 2, 253–262.