Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A NEW EXTENSION ON THE HARDY-HILBERT INEQUALITY

  • Zhou, Yu (Department of Mathematics and Computer Science Normal College, Jishou University) ;
  • Gao, Mingzhe (Department of Mathematics and Computer Science Normal College, Jishou University)
  • Received : 2011.05.09
  • Published : 2012.07.31
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Abstract

A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter ${\lambda}$ (with ${\lambda}>1-\frac{2}{pq}$) and a weight function of the form $x^{1-\frac{2}{r}}$ (with $r$ > 1). And the constant factors of new inequalities established are proved to be the best possible. In particular, for case $r$ = 2, a new Hilbert type inequality is obtained. As applications, an equivalent form is considered.

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References

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