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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