A Multiple Hilbert-Type Integral Inequality in the Whole Space

  • Bicheng YangEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 134)


In this paper, by introducing some interval variables and using the weight functions and the way of real analysis, a multiple Hilbert-type integral inequality in the whole space with a best possible constant factor is given, which is an extension of some published results. The equivalent forms, the operator expressions with the norm, the equivalent reverses, a few particular cases and some examples with the particular kernels are also considered.



This work is supported by the National Natural Science Foundation (No. 61772140), and Appropriative Researching Fund for Professors and Doctors, Guangdong University of Education (No. 2015ARF25). I am grateful for their help.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsGuangdong University of EducationGuangzhou, GuangdongPeople’s Republic of China

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