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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.
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참고문헌 (9)
참고문헌 신청
B. Yang / 2009 / The Norm of Operator and Hilbert-Type Inequalities / Beijing, Science Press
G. H. Hardy / 1952 / Inequalities / Cambridge Univ. Press
I. S. Gradshteyn / 2000 / Table of Integrals, Series, and Products / Academic Press
J. Kuang / 2000 / On new generalizations of Hilbert’s inequality and their ap- plications / J. Math. Anal. Appl 245 (1) : 248 ~ 265
M. Gao / 1997 / On Hilbert’s inequality and its applications / J. Math. Anal. Appl 22 (1) : 316 ~ 323
G. H. Hardy / 1952 / Inequalities / Cambridge Univ. Press
I. S. Gradshteyn / 2000 / Table of Integrals, Series, and Products / Academic Press
J. Kuang / 2000 / On new generalizations of Hilbert’s inequality and their ap- plications / J. Math. Anal. Appl 245 (1) : 248 ~ 265
M. Gao / 1997 / On Hilbert’s inequality and its applications / J. Math. Anal. Appl 22 (1) : 316 ~ 323
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