충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제31권2호
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  • Pages.231-237
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  • 2018
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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ON HARDY AND PÓLYA-KNOPP'S INEQUALITIES

  • Kwon, Ern Gun (Department of Mathematics Education Andong National University) ;
  • Jo, Min Ju (Department of Mathematics Graduate School, Andong National University)
  • 투고 : 2018.01.08
  • 심사 : 2018.03.13
  • 발행 : 2018.05.15
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초록

Hardy's inequality is refined non-trivially as the form $${\int_{0}^{{\infty}}}\{{\frac{1}{x}}{\int_{0}^{x}}f(t)dt\}^pdx{\leq}Q_f{\times}({\frac{p}{p-1}})^p{\int_{0}^{x}}f^p(x)dx$$ for some $Q_f:0{\leq}Q_f{\leq}1$. $P{\acute{o}}lya$-Knopp's inequality is also refined by the similar form.

키워드

참고문헌

  1. E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, Berlin, 1983.
  2. G. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, 1952.
  3. K. Hu, On an inequality and its applications, Sci. Sinica, 24 (1981), no. 8, 1047- 1055.
  4. K. Knopp, Uber reihen mit positiven gliedern, J. London Math. Soc. 3 (1928), 205-211.
  5. E. G. Kwon, On Carlesons inequality, Jour. Inequal. Appl. 2018 (2018), 2018:91, DOI10.1186/s13660-018-1682-2.
  6. E. G. Kwon and E. K. Bae, On a continuous form of Holder inequality, Jour. Math. Anal. Appl. 343 (2008), 585-592. https://doi.org/10.1016/j.jmaa.2008.01.057
  7. E. G. Kwon and J. E. Bae, On a generalized Holder inequality, Jour. Inequal. Appl. 2015 (2015), 2015:88 DOI10.1186/s13660-015-0612-9.
  8. E. G. Kwon and J. E. Bae, On a refined Holder's inequality, Jour. Math. Inequal. 10 (2016), 261-268.