A half-discrete Hilbert-type inequality in the whole plane related to the Riemann zeta function
- 7 April 2017
- journal article
- research article
- Published by Taylor & Francis Ltd in Applicable Analysis
- Vol. 97 (9), 1505-1525
- https://doi.org/10.1080/00036811.2017.1313411
Abstract
By the use of Hermite–Hadamard’s inequality and weight functions, a half-discrete Hilbert-type inequality in the whole plane with the kernel of hyperbolic cotangent function and multi-parameters is given. The constant factor related to the Riemann zeta function is proved to be the best possible. The equivalent forms, two kinds of particular inequalities, the operator expressions and some equivalent reverses are considered.Keywords
Funding Information
- National Natural Science Foundation of China (No. 61370186)
- Guangdong University of Education (Appropriative Researching Fund for Professors and)
- Universität Zürich (Forschungskredit grant (Grant Nr. FK-15-106), FK-15-106)
- University of Zurich (10.13039/501100001809)
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