On a class of Hilbert-type inequalities in the whole plane related to exponent function

Journal of inequalities and applications

Minghui You¹ 

[1] Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, 310053, Hangzhou, China;

关键词: Hilbert-type inequality;    Exponent function;    Partial fraction expansion;    Bernoulli number;    Euler number;    26D15;    26D10;    47B38;   

DOI  :  10.1186/s13660-021-02563-5

来源: Springer

【 摘 要 】

By introducing a kernel involving an exponent function with multiple parameters, we establish a new Hilbert-type inequality and its equivalent Hardy form. We also prove that the constant factors of the obtained inequalities are the best possible. Furthermore, by introducing the Bernoulli number, Euler number, and the partial fraction expansion of cotangent function and cosecant function, we get some special and interesting cases of the newly obtained inequality.

【 授权许可】

CC BY