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Best constants for certain multilinear integral operators

Journal of Inequalities and Applications volume 2006, Article number: 28582 (2006) Cite this article

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.

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References

  1. 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. 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

    MATH  MathSciNet  Article  Google Scholar 

  3. 3.

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

    MATH  MathSciNet  Article  Google Scholar 

  4. 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. 5.

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

    Google Scholar 

  6. 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. 7.

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

    Google Scholar 

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Author information

Affiliations

  1. Department of Mathematics, Western Washington University, 516 High Street, Bellingham, WA, 98225-9063, USA

    Árpád Bényi

  2. Department of Mathematics and Statistics, Lederle GRT, University of Massachusetts, Amherst, MA, 01003-9305, USA

    Choonghong Tadahiro Oh

Authors
  1. Árpád Bényi
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  2. Choonghong Tadahiro Oh
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Corresponding author

Correspondence to Árpád Bényi.

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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

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Keywords

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