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
On a New Generalization of Hardy–Hilbert's Inequality and Its Applications
✍ Scribed by Yang Bicheng; Lokenath Debnath
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 102 KB
- Volume
- 233
- Category
- Article
- ISSN
- 0022-247X
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By introducing three parameters A, B, and , we give some generalizations of Hilbert's integral inequality and its equivalent form with the best constant factors. We also consider their associated double series forms.
This paper deals with some new generalizations of Hardy's integral inequality. An improvement of some inequality is also presented.
## Abstract If __L__ is a continuous symmetric __n__‐linear form on a real or complex Hilbert space and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\widehat{L}$\end{document} is the associated continuous __n__‐homogeneous polynomial, then \documentclass{article}\use