In this paper, by using the Euler-Maclaurin expansion for the zeta function and estimating the weight function effectively, we derive an improvement of a Hilbert-type inequality proved by B.C. Yang.
On a relation between Hilbert’s inequality and a Hilbert-type inequality
✍ Scribed by Bicheng Yang
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 197 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0893-9659
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✦ Synopsis
In this work, by introducing some parameters and estimating the weight coefficient, a new inequality with a best constant factor is established, which is a relation between Hilbert's inequality and a Hilbert-type inequality. As applications, the reverse form and some particular results are considered.
📜 SIMILAR VOLUMES
In this paper, the weight coefficient of the form y n r 2 n q 1 with Ž . . n ) 0 is introduced. Improvements on Hilbert's inequality and the Hardy᎐ Littlewood inequality are established, and these results are extended. ᮊ 1997
In this note, it is shown that the Hardy᎐Hilbert inequality for double series can Ž . be improved by introducing a proper weight function of the form rsin rp y Ž . 1y1rr Ž Ž . . O n rn with O n ) 0 into either of the two single summations. When r r r s 2, the classical Hilbert inequality is improved