Abstract
Using weight functions, we obtain a half-discrete Hilbert-type inequality in the whole plane with the kernel of hyperbolic secant function and multi-parameters. The constant factor related to the Hurwitz zeta function is proved to be the best possible. We also consider equivalent forms, two kinds of particular inequalities, the operator expressions and some reverses.
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Acknowledgements
B. Yang: This work is supported by the National Natural Science Foundation (No. 61772140), and Science and Technology Planning Project Item of Guangzhou City (No. 201707010229). I would like to express my gratitude for this support.
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Rassias, M.T., Yang, B., Raigorodskii, A. (2020). On a Half-Discrete Hilbert-Type Inequality in the Whole Plane with the Kernel of Hyperbolic Secant Function Related to the Hurwitz Zeta Function. In: Raigorodskii, A., Rassias, M. (eds) Trigonometric Sums and Their Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-37904-9_11
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DOI: https://doi.org/10.1007/978-3-030-37904-9_11
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