Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane
By means of the technique of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related to the beta function is proved to be the best possible. As applications,...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/2691816 |
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| _version_ | 1832568054722068480 |
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| author | Dongmei Xin Bicheng Yang Aizhen Wang |
| author_facet | Dongmei Xin Bicheng Yang Aizhen Wang |
| author_sort | Dongmei Xin |
| collection | DOAJ |
| description | By means of the technique of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related to the beta function is proved to be the best possible. As applications, the case of the homogeneous kernel, the operator expressions, and a few corollaries are considered. |
| format | Article |
| id | doaj-art-152ad4eaaec943a49d78c99012376b0d |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-152ad4eaaec943a49d78c99012376b0d2025-02-03T00:59:49ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/26918162691816Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole PlaneDongmei Xin0Bicheng Yang1Aizhen Wang2Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, ChinaBy means of the technique of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related to the beta function is proved to be the best possible. As applications, the case of the homogeneous kernel, the operator expressions, and a few corollaries are considered.http://dx.doi.org/10.1155/2018/2691816 |
| spellingShingle | Dongmei Xin Bicheng Yang Aizhen Wang Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane Journal of Function Spaces |
| title | Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane |
| title_full | Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane |
| title_fullStr | Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane |
| title_full_unstemmed | Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane |
| title_short | Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane |
| title_sort | equivalent property of a hilbert type integral inequality related to the beta function in the whole plane |
| url | http://dx.doi.org/10.1155/2018/2691816 |
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