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  • Research Article
  • Open Access

Best constants for certain multilinear integral operators

Journal of Inequalities and Applications20062006:28582

  • Received: 7 December 2004
  • Accepted: 27 March 2005
  • Published:


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.


  • Special Function
  • Integral Operator
  • Explicit Formula
  • Function Gamma
  • Integral Inequality


Authors’ Affiliations

Department of Mathematics, Western Washington University, 516 High Street, Bellingham, WA 98225-9063, USA
Department of Mathematics and Statistics, Lederle GRT, University of Massachusetts, Amherst, MA 01003-9305, USA


  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.2001.3804MATHMathSciNetView ArticleGoogle Scholar
  3. Hardy GH: Note on a theorem of Hilbert. Mathematische Zeitschrift 1920,6(3–4):314–317. 10.1007/BF01199965MATHMathSciNetView ArticleGoogle 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/s2-23.1.45Google Scholar
  5. Hardy GH, Littlewood JE, Pólya G: Inequalities. 2nd edition. Cambridge University Press, Cambridge; 1952:xii+324.MATHGoogle 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.MATHMathSciNetGoogle Scholar
  7. Weyl H: Singülare Integralgleichungen mit besonderer Berücksichtigung des Fourierschen Integraltheorems, Inaugural-Dissertation. , Gottingen; 1908.Google Scholar


© Bényi and Oh 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.