The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of <inline-formula> <graphic file="1029-242X-2008-917392-i1.gif"/></inline-formula>-Degree
<p>Abstract</p> <p>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 <inline-formula> <graphic file="1029-242X-2008-9...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2008-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2008/917392 |
| Summary: | <p>Abstract</p> <p>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 <inline-formula> <graphic file="1029-242X-2008-917392-i2.gif"/></inline-formula>-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.</p> |
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| ISSN: | 1025-5834 1029-242X |