A NEW EXTENSION ON THE HARDY-HILBERT INEQUALITY
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A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter λ (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.
Abstract
A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter λ (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.
참고문헌 (9)
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