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 A new extension on the Hardy-Hilbert inequality Commun. Korean Math. Soc. 2012 Vol. 27, No. 3, 547-556 https://doi.org/10.4134/CKMS.2012.27.3.547Printed September 1, 2012 Yu Zhou and Mingzhe Gao Normal College, Jishou University, Normal College, Jishou University Abstract : A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter $\lambda$ (with $\lambda>1-{2 \over {pq}}$) and a weight function of the form $x^{1-{2 \over r}}$ (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. Keywords : Hardy-Hilbert type inequality, double series, Euler-Maclaurin summation formula, weight function MSC numbers : 26D15 Downloads: Full-text PDF

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