Skip to main content
  • Research Article
  • Open access
  • Published:

Best constants for certain multilinear integral operators

Abstract

We provide explicit formulas in terms of the special function gamma for the best constants in nontensorial multilinear extensions of some classical integral inequalities due to Hilbert, Hardy, and Hardy-Littlewood-Pólya.

[1234567]

References

  1. Andrews GE, Askey R, Roy R: Special Functions, Encyclopedia of Mathematics and Its Applications. Volume 71. Cambridge University Press, Cambridge; 1999:xvi+664.

    Google Scholar 

  2. Grafakos L, Torres RH: A multilinear Schur test and multiplier operators. Journal of Functional Analysis 2001,187(1):1–24. 10.1006/jfan.2001.3804

    Article  MATH  MathSciNet  Google Scholar 

  3. Hardy GH: Note on a theorem of Hilbert. Mathematische Zeitschrift 1920,6(3–4):314–317. 10.1007/BF01199965

    Article  MATH  MathSciNet  Google Scholar 

  4. Hardy GH: Note on a theorem of Hilbert concerning series of positive terms. Proceedings of the London Mathematical Society 1925, 23: 45–46. 10.1112/plms/s2-23.1.45

    Google Scholar 

  5. Hardy GH, Littlewood JE, Pólya G: Inequalities. 2nd edition. Cambridge University Press, Cambridge; 1952:xii+324.

    MATH  Google Scholar 

  6. Schur I: Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen veränderlichen. Journal für die Reine und Angewandte Mathematik 1911, 140: 1–28.

    MATH  MathSciNet  Google Scholar 

  7. Weyl H: Singülare Integralgleichungen mit besonderer Berücksichtigung des Fourierschen Integraltheorems, Inaugural-Dissertation. , Gottingen; 1908.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Árpád Bényi.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Bényi, Á., Oh, C.T. Best constants for certain multilinear integral operators. J Inequal Appl 2006, 28582 (2006). https://doi.org/10.1155/JIA/2006/28582

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/JIA/2006/28582

Keywords