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On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of1-Order and Applications

Abstract

Some character of the symmetric homogenous kernel of1-order in Hilbert-type operator is obtained. Two equivalent inequalities with the symmetric homogenous kernel of-order are given. As applications, some new Hilbert-type inequalities with the best constant factors and the equivalent forms as the particular cases are established.

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References

  1. 1.

    Yang B: On the norm of a Hilbert's type linear operator and applications. Journal of Mathematical Analysis and Applications 2007,325(1):529–541. 10.1016/j.jmaa.2006.02.006

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Yang B: On the norm of a self-adjoint operator and applications to the Hilbert's type inequalities. Bulletin of the Belgian Mathematical Society 2006,13(4):577–584.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Yang B: On the norm of an integral operator and applications. Journal of Mathematical Analysis and Applications 2006,321(1):182–192. 10.1016/j.jmaa.2005.07.071

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Yang B: On the norm of a self-adjoint operator and a new bilinear integral inequality. Acta Mathematica Sinica 2007,23(7):1311–1316. 10.1007/s10114-005-0895-8

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Bényi Á, Oh C: Best constants for certain multilinear integral operators. Journal of Inequalities and Applications 2006, 2006: 12 pages.

    Article  Google Scholar 

  6. 6.

    Yang B: On the norm of a certain self-adjiont integral operator and applications to bilinear integral inequalities. to appear in Taiwanese Journal of Mathematics to appear in Taiwanese Journal of Mathematics

  7. 7.

    Wang Z, Gua D: An Introduction to Special Functions. Science Press, Bejing, China; 1979.

    Google Scholar 

  8. 8.

    Yang B: Generalization of a Hilbert-type inequality with the best constant factor and its applications. Journal of Mathematical Research and Exposition 2005,25(2):341–346.

    MathSciNet  MATH  Google Scholar 

  9. 9.

    Yang B: On new generalizations of Hilbert's inequality. Journal of Mathematical Analysis and Applications 2000,248(1):29–40. 10.1006/jmaa.2000.6860

    MathSciNet  Article  MATH  Google Scholar 

  10. 10.

    Yang B: An extension of Hardy-Hilbert's inequality. Chinese Annals of Mathematics 2002,23(2):247–254.

    MathSciNet  MATH  Google Scholar 

  11. 11.

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

    Google Scholar 

  12. 12.

    Yang B: On a generalization of a Hilbert's type inequality and its applications. Chinese Journal of Engineering Mathematics 2004,21(5):821–824.

    MathSciNet  MATH  Google Scholar 

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Correspondence to Bicheng Yang.

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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.

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Yang, B. On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of1-Order and Applications. J Inequal Appl 2007, 047812 (2007). https://doi.org/10.1155/2007/47812

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Keywords

  • Constant Factor
  • Equivalent Form
  • Homogenous Kernel
  • Equivalent Inequality
  • Good Constant Factor
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