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On Hilbert-type Integral Inequalities with the Homogenous Kernel of -4- degree

Bing He|Qiliang Huang
경북대학교 자연과학대학 수학과|2009.09|Kyungpook Mathematical Journal|제49권 제3호|pp. 521-532

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키워드

kernelweight functionHilbert-type integral inequalityequivalent formreverse form
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초록

In this paper, by introducing a homogenous kernel of -4-degree, we establish a new Hilbert-type integral inequality with multi-parameter and a best constant factor. As applications, the equivalent form, the reverse forms and some particular results are given correspondingly.

Abstract

In this paper, by introducing a homogenous kernel of -4-degree, we establish a new Hilbert-type integral inequality with multi-parameter and a best constant factor. As applications, the equivalent form, the reverse forms and some particular results are given correspondingly.

참고문헌 (12)

  1. G. H. Hardy, "Inequalities" (1952), Cambridge Univ. Press
  2. D. S. Mitrinovic, "Inequalities involving functions and their integrals and derivatives" (1991), Kluwer Acad. Publ
  3. B. Yang, "On Hilbert's integral inequality", J. Math. Anal. Appl, 220, pp.778~785 (1998)
  4. B. Yang, "A Note on Hilbert's Integral Inequalities", Chin Quar. J. Math, 13(4), pp.83~86 (1998)
  5. B. Yang, "On the Extended Hardy-Hilbert's Inequality", J. Math. Anal. Appl, 272(1), pp.187~199 (2002)
  6. B. Yang, "Generalization of Hilbert and Hardy-Hilbert integral inequalities", Math. Ineq. Appl, 8(2), pp.259~272 (2005)
  7. Y. Hong, "On Hardy-Hilbert integral inequalities with some parameters", J. Ineq. in Pure and Applied Math, 6(4), pp.1~10 (2005)
  8. B. Yang, "On Hilbert's Inequality with Some Parameters", Acta Mathematica Sinica, 49(5), pp.1121~1126 (2006)
  9. B. Yang, "On a Reverse of Hardy-Hilbert's Integral Inequality", Pure and Applied Mathematics, 22(3), pp.312~317 (2006)
  10. B. Yang, "A Bilinear Inequality with the Kernal of -2-order Homogeneous", Journal of Xiamen University(Natural Science), 45(6), pp.752~755 (2006)
  11. Z. Xie, "A Hilbert-type integral inequality whose kernel is a homogeneous form of degree -3", J. Math. Anal. Appl, 339(1), pp.324~331 (2007)
  12. J. Kuang, "Applied inequalities" (2004), Shandong Science and Technology Press

관련 논문AI추천

On a New Hilbert-type Integral InequalityDongmei Xin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제2호A New Hilbert-type Integral Inequality with Some Parametersand Its ReverseBicheng Yang, Zitian Xie경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제1호The Hilbert-type Integral Inequality with the System Kernel of -λ Degree Homogeneous FormZheng Zeng, Zitian Xie경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제2호Hilbert-Type Integral Inequalities in the Whole Plane with the Non-homogeneous KernelDongmei Xin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호On a Relation to Hilbert’s Integral Inequality and a Hilbert- Type InequalityBicheng Yang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호On Certain Extension of Hilbert’s Integral Inequality with Best ConstantsBing He, Yongjin Li, Yu Lin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제3호

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