The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of -Degree
© Wuyi Zhong. 2008
Received: 24 March 2008
Accepted: 19 May 2008
Published: 20 May 2008
By introducing an integral operator, a norm with a weight function, and two pairs of conjugate exponents, we find the conditions for the Hilbert-type integral inequalities with a homogeneous kernel of -degree. We also prove that the constant factors in the inequalities are all the best possible. As the particular situations, some new inequalities with a homogeneous kernel and their other two forms are given. We extend some previous results.
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