A NEW EXTENSION ON THE HARDY-HILBERT INEQUALITY

Title & Authors
A NEW EXTENSION ON THE HARDY-HILBERT INEQUALITY
Zhou, Yu; Gao, Mingzhe;

Abstract
A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter $\small{{\lambda}}$ (with $\small{{\lambda}}$>$\small{1-\frac{2}{pq}}$) and a weight function of the form $\small{x^{1-\frac{2}{r}}}$ (with $\small{r}$ > 1). And the constant factors of new inequalities established are proved to be the best possible. In particular, for case $\small{r}$
Keywords
Hardy-Hilbert type inequality;double series;Euler-Maclaurin summation formula;weight function;
Language
English
Cited by
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