Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel
Let Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ℝ+m ∑n=1∞ Kn,xm,ρanfxdx≤Ma~p...
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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/10.1155/2020/7414861 |
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| _version_ | 1849468849518280704 |
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| author | Qiang Chen Bing He Yong Hong Zhen Li |
| author_facet | Qiang Chen Bing He Yong Hong Zhen Li |
| author_sort | Qiang Chen |
| collection | DOAJ |
| description | Let Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ℝ+m ∑n=1∞ Kn,xm,ρanfxdx≤Ma~p,αfq,β are discussed. Finally, its applications in operator theory are discussed. |
| format | Article |
| id | doaj-art-f47c67553b3e4a3391a28d5a2c9b3da3 |
| 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-f47c67553b3e4a3391a28d5a2c9b3da32025-08-20T03:25:43ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/74148617414861Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous KernelQiang Chen0Bing He1Yong Hong2Zhen Li3Department of Computer Science, Guangdong University of Education, Guangzhou 510303, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaDepartment of Mathematics, Guangdong Baiyun University, Guangzhou 510450, ChinaCollege of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, Guangdong 510320, ChinaLet Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ℝ+m ∑n=1∞ Kn,xm,ρanfxdx≤Ma~p,αfq,β are discussed. Finally, its applications in operator theory are discussed.http://dx.doi.org/10.1155/2020/7414861 |
| spellingShingle | Qiang Chen Bing He Yong Hong Zhen Li Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel Journal of Function Spaces |
| title | Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel |
| title_full | Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel |
| title_fullStr | Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel |
| title_full_unstemmed | Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel |
| title_short | Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel |
| title_sort | equivalent parameter conditions for the validity of half discrete hilbert type multiple integral inequality with generalized homogeneous kernel |
| url | http://dx.doi.org/10.1155/2020/7414861 |
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