- Research Article
- Open Access
A Hilbert's Inequality with a Best Constant Factor
© Z. Zeng and Z.-t. Xie. 2009
- Received: 6 February 2009
- Accepted: 23 July 2009
- Published: 23 August 2009
We give a new Hilbert's inequality with a best constant factor and some parameters.
- Constant Factor
- Weight Coefficient
- Equivalent Form
- Strict Inequality
- Integral Inequality
where the constant factors are all the best possible . It attracted some attention in the recent years. Actually, inequalities (1.1) and (1.2) have many generalizations and variants. Equation (1.1) has been strengthened by Yang and others ( including integral inequalities ) [2–11].
In 2006, Yang gave an extension of  as follows.
In 2007 Xie gave a new Hilbert-type Inequality  as follows.
The main objective of this paper is to build a new Hilbert's inequality with a best constant factor and some parameters.
In the following, we always suppose that
The lemma is proved.
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