On a class of Hilbert-type inequalities in the whole plane involving some classical kernel functions

• Published in: Proceedings of the Edinburgh Mathematical Society Vol. 65; no. 3; pp. 833 - 846
• Main Author: You, Minghui
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.08.2022
• Subjects: Inequalities; Inequality; Kernel functions; Mathematical functions; Weighting functions; 47B38; weight function; classical kernel functions; 26D10; partial fraction expansion; Hilbert-type inequality; whole plane; 26D15

In this paper, by the introduction of several parameters, we construct a new kernel function which is defined in the whole plane and includes some classical kernel functions. Estimating the weight functions with the techniques of real analysis, we establish a new Hilbert-type inequality in the whole...