On Hilbert's Inequality for Double Series and Its Applications
This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u(x) and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applicatio...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/165089 |
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| _version_ | 1832561987312156672 |
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| author | Zhou Yu Gao Mingzhe |
| author_facet | Zhou Yu Gao Mingzhe |
| author_sort | Zhou Yu |
| collection | DOAJ |
| description | This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u(x) and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality in Hp function are given. |
| format | Article |
| id | doaj-art-85dd635ca7a04ec2b615122ef0d498e6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-85dd635ca7a04ec2b615122ef0d498e62025-02-03T01:23:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/165089165089On Hilbert's Inequality for Double Series and Its ApplicationsZhou Yu0Gao Mingzhe1Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou, Hunan 416000, ChinaDepartment of Mathematics and Computer Science, Normal College of Jishou University, Jishou, Hunan 416000, ChinaThis study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u(x) and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality in Hp function are given.http://dx.doi.org/10.1155/2008/165089 |
| spellingShingle | Zhou Yu Gao Mingzhe On Hilbert's Inequality for Double Series and Its Applications International Journal of Mathematics and Mathematical Sciences |
| title | On Hilbert's Inequality for Double Series and Its Applications |
| title_full | On Hilbert's Inequality for Double Series and Its Applications |
| title_fullStr | On Hilbert's Inequality for Double Series and Its Applications |
| title_full_unstemmed | On Hilbert's Inequality for Double Series and Its Applications |
| title_short | On Hilbert's Inequality for Double Series and Its Applications |
| title_sort | on hilbert s inequality for double series and its applications |
| url | http://dx.doi.org/10.1155/2008/165089 |
| work_keys_str_mv | AT zhouyu onhilbertsinequalityfordoubleseriesanditsapplications AT gaomingzhe onhilbertsinequalityfordoubleseriesanditsapplications |