A Note on Hilbert's Inequality
โ Scribed by Ingham, A. E.
- Book ID
- 120100069
- Publisher
- Oxford University Press
- Year
- 1936
- Tongue
- English
- Weight
- 97 KB
- Volume
- s1-11
- Category
- Article
- ISSN
- 0024-6107
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this note, it is shown that the HardyแHilbert inequality for double series can ลฝ . be improved by introducing a proper weight function of the form rsin rp y ลฝ . 1y1rr ลฝ ลฝ . . 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
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 considere