Abstract
By the use of the methods of real analysis and the weight functions, a few equivalent conditions of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The best possible constant factor is related to the extended Riemann zeta function. As applications, a few equivalent conditions of a Hilbert-type integral inequality with the homogeneous kernel in the whole plane are deduced. We also consider the operator expressions and a few particular cases.
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Acknowledgements
This work is supported by the National Natural Science Foundation (Nos. 61370186, 61640222), and Appropriative Researching Fund for Professors and Doctors, Guangdong University of Education (No. 2015ARF25). we are grateful for this help.
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Rassias, M.T., Yang, B. (2019). On a Hilbert-Type Integral Inequality in the Whole Plane Related to the Extended Riemann Zeta Function. In: Rassias, T., Pardalos, P. (eds) Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-030-31339-5_19
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DOI: https://doi.org/10.1007/978-3-030-31339-5_19
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