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  • Research Article
  • Open Access

The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of -Degree

Journal of Inequalities and Applications20082008:917392

  • Received: 24 March 2008
  • Accepted: 19 May 2008
  • Published:


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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Authors’ Affiliations

Department of Mathematics, Guangdong Institute of Education, Guangzhou, Guangdong, 510303, China