On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel
We build a multiple Hilbert-type integral inequality with the symmetric kernel K(x,y) and involving an integral operator T. For this objective, we introduce a norm ∥x∥αn  (x∈â„Â+n), two pairs of conjugate exponents (p,q) and (r,s), and two parameters. As applications, t...
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| Format: | Article |
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SpringerOpen
2007-11-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2007/27962 |
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doaj-7776cbd88dbf4de7a014f1f65eac52ed2020-11-24T21:10:43ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2007-11-01200710.1155/2007/27962On a Multiple Hilbert-Type Integral Inequality with the Symmetric KernelBicheng YangWuyi ZhongWe build a multiple Hilbert-type integral inequality with the symmetric kernel K(x,y) and involving an integral operator T. For this objective, we introduce a norm ∥x∥αn  (x∈â„Â+n), two pairs of conjugate exponents (p,q) and (r,s), and two parameters. As applications, the equivalent form, the reverse forms, and some particular inequalities are given. We also prove that the constant factors in the new inequalities are all the best possible.http://dx.doi.org/10.1155/2007/27962 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Bicheng Yang Wuyi Zhong |
| spellingShingle |
Bicheng Yang Wuyi Zhong On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel Journal of Inequalities and Applications |
| author_facet |
Bicheng Yang Wuyi Zhong |
| author_sort |
Bicheng Yang |
| title |
On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel |
| title_short |
On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel |
| title_full |
On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel |
| title_fullStr |
On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel |
| title_full_unstemmed |
On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel |
| title_sort |
on a multiple hilbert-type integral inequality with the symmetric kernel |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2007-11-01 |
| description |
We build a multiple Hilbert-type integral inequality with the symmetric kernel K(x,y) and involving an integral operator T. For this objective, we introduce a norm ∥x∥αn  (x∈â„Â+n), two pairs of conjugate exponents (p,q) and (r,s), and two parameters. As applications, the equivalent form, the reverse forms, and some particular inequalities are given. We also prove that the constant factors in the new inequalities are all the best possible. |
| url |
http://dx.doi.org/10.1155/2007/27962 |
| work_keys_str_mv |
AT bichengyang onamultiplehilberttypeintegralinequalitywiththesymmetrickernel AT wuyizhong onamultiplehilberttypeintegralinequalitywiththesymmetrickernel |
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1716755587990028288 |