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

By W. Zhong. 2008

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/59ab666e35fae807feed65b2cbdaa9b36a069db1