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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 849-859, October 2007




A NEW HILBERT'S TYPE INTEGRAL INEQUALITY


BY


BICHENG YANG




Abstract. This paper deals with a new Hilbert's type integral inequality by introducing a parameter and the Beta function. As applications, the reversions, the equivalent forms and some particular results are considered. All the theorems provide some new estimates on this type of inequalities.

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Received October 15, 2006; revised January 25, 2007.

AMS Subject Classification. 26D15.

Key words. Hilbert's integral inequality, weight function, Beta function.