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 |
| Published: |
SpringerOpen
2008-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2008/917392 |
| _version_ | 1811278572895076352 |
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| author | Zhong Wuyi |
| author_facet | Zhong Wuyi |
| author_sort | Zhong Wuyi |
| collection | DOAJ |
| description | <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> |
| first_indexed | 2024-04-13T00:38:16Z |
| format | Article |
| id | doaj.art-d78a80ab6fd54228b5ab065d7f665786 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-04-13T00:38:16Z |
| publishDate | 2008-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d78a80ab6fd54228b5ab065d7f6657862022-12-22T03:10:17ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2008-01-0120081917392The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of <inline-formula> <graphic file="1029-242X-2008-917392-i1.gif"/></inline-formula>-DegreeZhong Wuyi<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>http://www.journalofinequalitiesandapplications.com/content/2008/917392 |
| spellingShingle | Zhong Wuyi The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of <inline-formula> <graphic file="1029-242X-2008-917392-i1.gif"/></inline-formula>-Degree Journal of Inequalities and Applications |
| title | The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of <inline-formula> <graphic file="1029-242X-2008-917392-i1.gif"/></inline-formula>-Degree |
| title_full | The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of <inline-formula> <graphic file="1029-242X-2008-917392-i1.gif"/></inline-formula>-Degree |
| title_fullStr | The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of <inline-formula> <graphic file="1029-242X-2008-917392-i1.gif"/></inline-formula>-Degree |
| title_full_unstemmed | The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of <inline-formula> <graphic file="1029-242X-2008-917392-i1.gif"/></inline-formula>-Degree |
| title_short | The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of <inline-formula> <graphic file="1029-242X-2008-917392-i1.gif"/></inline-formula>-Degree |
| title_sort | hilbert type integral inequalities with a homogeneous kernel of inline formula graphic file 1029 242x 2008 917392 i1 gif inline formula degree |
| url | http://www.journalofinequalitiesandapplications.com/content/2008/917392 |
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