On Hilbert-Pachpatte Multiple Integral Inequalities
© Changjian Zhao et al. 2010
Received: 11 March 2010
Accepted: 28 July 2010
Published: 10 August 2010
We establish some multiple integral Hilbert-Pachpatte-type inequalities. As applications, we get some inverse forms of Pachpatte's inequalities which were established in 1998.
In 1934, Hilbert  established the following well-known integral inequality.
In recent years, considerable attention has been given to various extensions and improvements of the Hilbert inequality form different viewpoints [2–10]. In particular, Pachpatte  proved some inequalities similar to Hilbert's integral inequalities in 1998. In this paper, we establish some new multiple integral Hilbert-Pachpatte-type inequalities.
2. Main Results
The proof is complete.
This completes the proof of Theorem 2.3.
This paper is supported by the National Natural Sciences Foundation of China (10971205). This paper is partially supported by the Research Grants Council of the Hong Kong SAR, China (Project no. HKU7016/07P) and an HKU Seed Grant for Basic Research.
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