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A New Multiple Hilbert-Type Integral Inequality With A Non-Homogeneous Form

Zheng Zeng*, Xie Zitian**

* Professor, Foshan University, Foshan, Guangdong, China.

** Professor and Executive Director, Foshan University, Foshan, Guangdong, China.

Periodicity:July - September'2015
DOI : https://doi.org/10.26634/jmat.4.3.3597

Abstract

Hilbert-type inequalities are important in analysis and its applications. In recent years, some authors have studied and published a few Hilbert-type multiple integral inequalities, which are hard and interesting. In this paper, by estimating the weight function and technique of real analysis, the authors give a new multiple Hilbert-type integral inequality with a non-Homogeneous form as, F(x,y) f(x)g(y)dxdy < K f g (p >1). The best possible Rn+ x Rn+ p,w q,w constant factor is given, and the equivalent form is also considered. Many particular cases of Hilbert-type integral inequality with a non-homogeneous form are included. As its applications, the authors have considered some particular results.

Keywords

Multiple Hilbert-Type Integral Inequality, Weight Function, Ho lder's Inequality, Non-Homogeneous Form

How to Cite this Article?

Zeng, Z., and Xie, Z. (2015). A New Multiple Hilbert-Type Integral Inequality with A Non-Homogeneous Form. i-manager’s Journal on Mathematics, 4(3), 25-34. https://doi.org/10.26634/jmat.4.3.3597

References

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