Abstract
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.
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Acknowledgements
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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Yang, B. (2018). A Multiple Hilbert-Type Integral Inequality in the Whole Space. In: Rassias, T. (eds) Applications of Nonlinear Analysis . Springer Optimization and Its Applications, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-89815-5_27
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DOI: https://doi.org/10.1007/978-3-319-89815-5_27
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