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The Hilbert-type Integral Inequality with the System Kernel of -λ Degree Homogeneous Form

Zitian Xie|Zheng Zeng
경북대학교 자연과학대학 수학과|2010.06|Kyungpook Mathematical Journal|제50권 제2호|pp. 297-306

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참고문헌

키워드

weight functionHÄolder's inequality
주제분류수학

초록

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree -λ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.

Abstract

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree -λ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.

참고문헌 (22)

  1. Hardy G. H., "Inequalities" (1952), Cambridge University Press
  2. Bicheng Yang, "On the the norm of an intergal operator and applications", J. Math. Anal. Appl., 321, pp.182~192 (2006)
  3. Zitian Xie, "A Hilbert-type integral inequality whose kernel is a ho-mogeneous form of degree -3", J.Math.Appl., (339), pp.324~331 (2008)
  4. Zitian Xie, "A Hilbert-type inequality with parameters", Natural science Journal of Xiangtan University, 29(3), pp.24~28 (2007)
  5. Bicheng Yang, "A Hilbert-type inequality with a mixed kemel and extensions", Journalof Sichuan Normal University (Natural Science), 31(3), pp.281~284 (2008)
  6. Zitian Xie, "A Generalization of a Hilbert-type inequality with a best constant factor", Journal of Sichuan Normal University (Natural Science), 32(5), pp.626~629 (2009)
  7. Zitian Xie, "A new Hilbert-type integral inequality with a best constant factor", J. Wuhan Univ. (Nat.Sci.Ed), 55(6), pp.637~640 (2009)
  8. Zitian Xie, "A new Hilbert-type integral inequality and its reverse", Journal of Henan University (Science Edition), 39(1), pp.10~13 (2009)
  9. Zitian Xie, "A New Hilbert-type Integral Inequality with Some Parametersand Its Reverse", Kyungpook Mathematical Journal, 48(1), pp.93~100 (2008), 경북대학교 자연과학대학 수학과
  10. Bicheng Yang, "On a Hilbert-type integral inequality with multiple-parameters", Journal of Southwest China Normal University(Natural Science), 32(5), pp.33~38 (2007)
  11. Bicheng Yang, "A relation to Hilbert's integral inequality and some base Hilbert-type inequalities", Journal of inequalities in pure and applied mathematics, 9(2), pp.1~8 (2008)
  12. Bicheng Yang, "A base Hilbert-type integral inequality with the homogeneous kernel of -1-degree and extensions", Journal of Guangong Education Institute, 28(3), pp.5~10 (2008)
  13. Dongmei Xin, "On a New Hilbert-type Integral Inequality", Kyungpook Mathematical Journal, 49(2), pp.393~401 (2009), 경북대학교 자연과학대학 수학과
  14. Wuyi Zhong, "A reverse Hilbert's type integral inequality with some parameters and the equalent forms", Pure and Applied Mathematics, 24(2), pp.401~407 (2008)
  15. Bicheng Yang, "On a Hilbert-type integral inequality with a parameter", Pure and Ap-plied Mathematics, 24(3), pp.489~494 (2008)
  16. Bicheng Yang, "A new Hilbert-type integral inequality", Journal of Jilin University (Sci-ence Edition), 45(1), pp.63~67 (2007)
  17. Bicheng Yang, "A Hilbert-type integral inequality", Journal of Zhejiang University (Sci-ence Edition), 34(2), pp.121~124 (2007)
  18. Bicheng Yang, "An extension of the Hilbert's type integral inequality and its applica-tions", J. of Math., 27(3), pp.285~290 (2007)
  19. Bicheng Yang, "On a Reverse Hardy-Hilbert's Inequality", Kyungpook Mathematical Journal, 47(3), pp.411~423 (2007), 경북대학교 자연과학대학 수학과
  20. Zitian Xie, "A New Hilbert type Inequality with some parameters", Journal of South China Normal University (Natural Science Edition), 120(2), pp.38~42 (2008)
  21. Zitian Xie, "A reverse Hilbert-type inequality with a best constant Factor", J. Math. Anal. Appl., 343, pp.1154~1160 (2008)
  22. Jichang Kang, "Applied Inequalities" (2004), Shangdong Science and Technology press

관련 논문AI추천

On Hilbert-type Integral Inequalities with the Homogenous Kernel of -4- degreeBing He, Qiliang Huang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호On a New Hilbert-type Integral InequalityDongmei Xin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제2호On Certain Extension of Hilbert’s Integral Inequality with Best ConstantsBing He, Yongjin Li, Yu Lin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제3호A New Hilbert-type Integral Inequality with Some Parametersand Its ReverseBicheng Yang, Zitian Xie경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제1호Hilbert-Type Integral Inequalities in the Whole Plane with the Non-homogeneous KernelDongmei Xin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호On a Bilateral Hilbert-Type Inequality with a Homogeneous Kernel of 0-DegreeBing He경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제2호

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