• 제목/요약/키워드: Hardy inequality

검색결과 37건 처리시간 0.025초

APPLICATIONS OF TAYLOR SERIES FOR CARLEMAN'S INEQUALITY THROUGH HARDY INEQUALITY

  • IDDRISU, MOHAMMED MUNIRU;OKPOTI, CHRISTOPHER ADJEI
    • Korean Journal of Mathematics
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    • 제23권4호
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    • pp.655-664
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    • 2015
  • In this paper, we prove the discrete Hardy inequality through the continuous case for decreasing functions using elementary properties of calculus. Also, we prove the Carleman's inequality through limiting the discrete Hardy inequality with applications of Taylor series.

On an Extension of Hardy-Hilbert's Inequality

  • Yang, Bicheng
    • Kyungpook Mathematical Journal
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    • 제46권3호
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    • pp.425-431
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    • 2006
  • In this paper, by introducing three parameters A, B and ${\lambda}$, and estimating the weight coefficient, we give a new extension of Hardy-Hilbert's inequality with a best constant factor, involving the Beta function. As applications, we consider its equivalent inequality.

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On a Reverse Hardy-Hilbert's Inequality

  • Yang, Bicheng
    • Kyungpook Mathematical Journal
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    • 제47권3호
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    • pp.411-423
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    • 2007
  • This paper deals with a reverse Hardy-Hilbert's inequality with a best constant factor by introducing two parameters ${\lambda}$ and ${\alpha}$. We also consider the equivalent form and the analogue integral inequalities. Some particular results are given.

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WEIGHTED HARDY INEQUALITIES WITH SHARP CONSTANTS

  • Kalybay, Aigerim;Oinarov, Ryskul
    • 대한수학회지
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    • 제57권3호
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    • pp.603-616
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    • 2020
  • In the paper, we establish the validity of the weighted discrete and integral Hardy inequalities with periodic weights and find the best possible constants in these inequalities. In addition, by applying the established discrete Hardy inequality to a certain second-order difference equation, we discuss some oscillation and nonoscillation results.

THE HARDY TYPE INEQUALITY ON METRIC MEASURE SPACES

  • Du, Feng;Mao, Jing;Wang, Qiaoling;Wu, Chuanxi
    • 대한수학회지
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    • 제55권6호
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    • pp.1359-1380
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    • 2018
  • In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.