A new extension on the Hardy-Hilbert inequality
Commun. Korean Math. Soc. 2012 Vol. 27, No. 3, 547-556
Printed 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
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