The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of −λ-Degree
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 −λ-degree. We also prove that the constant factors in the inequalities are all the best pos...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2008-06-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/917392 |
| Summary: | 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 −λ-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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| ISSN: | 1025-5834 1029-242X |