Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding
Let ∑i=1n1/pi=1pi>1, in this paper, by using the method of weight functions and technique of real analysis; it is proved that the equivalent parameter condition for the validity of multiple integral Hilbert-type inequality ∫R+nKx1,⋯,xn∏i=1nfixi dx1⋯dxn≤M∏i=1nfipi,αi with homogeneous kernel Kx1,⋯,...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/3050952 |
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| _version_ | 1832550539251941376 |
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| author | Jianquan Liao Yong Hong Bicheng Yang |
| author_facet | Jianquan Liao Yong Hong Bicheng Yang |
| author_sort | Jianquan Liao |
| collection | DOAJ |
| description | Let ∑i=1n1/pi=1pi>1, in this paper, by using the method of weight functions and technique of real analysis; it is proved that the equivalent parameter condition for the validity of multiple integral Hilbert-type inequality ∫R+nKx1,⋯,xn∏i=1nfixi dx1⋯dxn≤M∏i=1nfipi,αi with homogeneous kernel Kx1,⋯,xn of order λ is ∑i=1nαi/pi=λ+n−1, and the calculation formula of its optimal constant factor is obtained. The basic theory and method of constructing a Hilbert-type multiple integral inequality with the homogeneous kernel and optimal constant factor are solved. |
| format | Article |
| id | doaj-art-240e281560ff4585986aa3090e61d55b |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-240e281560ff4585986aa3090e61d55b2025-02-03T06:06:31ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/30509523050952Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality HoldingJianquan Liao0Yong Hong1Bicheng Yang2Department of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaDepartment of Mathematics, Guangdong Baiyun University, Guangzhou 510450, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaLet ∑i=1n1/pi=1pi>1, in this paper, by using the method of weight functions and technique of real analysis; it is proved that the equivalent parameter condition for the validity of multiple integral Hilbert-type inequality ∫R+nKx1,⋯,xn∏i=1nfixi dx1⋯dxn≤M∏i=1nfipi,αi with homogeneous kernel Kx1,⋯,xn of order λ is ∑i=1nαi/pi=λ+n−1, and the calculation formula of its optimal constant factor is obtained. The basic theory and method of constructing a Hilbert-type multiple integral inequality with the homogeneous kernel and optimal constant factor are solved.http://dx.doi.org/10.1155/2020/3050952 |
| spellingShingle | Jianquan Liao Yong Hong Bicheng Yang Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding Journal of Function Spaces |
| title | Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding |
| title_full | Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding |
| title_fullStr | Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding |
| title_full_unstemmed | Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding |
| title_short | Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding |
| title_sort | equivalent conditions of a hilbert type multiple integral inequality holding |
| url | http://dx.doi.org/10.1155/2020/3050952 |
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