Communications of the
Korean Mathematical Society CKMS

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