Abstract:By introducing some parameters, we construct a non-homogeneous kernel function including hyperbolic functions on the whole plane. In addition, by using the rational fraction expansion of tangent function, a Hilbert-type integral inequality associated with the best possible constant factor and the higher derivatives of tangent function is presented. Furthermore, some meaningful and special results are presented by specializing the parameters with different values as on application.
有名辉, 孙霞. 一个R2上含双曲函数核的Hilbert型不等式[J]. 浙江大学学报(理学版), 2020, 47(5): 554-558.
YOU Minghui, SUN Xia. A Hilbert-type inequality defined on R2 with the kernel involving hyperbolic functions. Journal of ZheJIang University(Science Edition), 2020, 47(5): 554-558.
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