A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function

• Published in: Journal of inequalities and applications Vol. 2023; no. 1; pp. 43 - 15
• Main Author: You, Minghui
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 24.03.2023; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Half-discrete; Hardy-type inequality; Hilbert-type inequality; Homogeneous kernel; Inequalities; Inequality; Kernel functions; Mathematics; Mathematics and Statistics; Nonhomogeneous kernel; Parameters; Weighting functions; 47B38; 26D10; Nonhomogeneous kernel; Hardy-type inequality; Hilbert-type inequality; Half-discrete; Homogeneous kernel; 26D15

In this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the homogeneous and the nonhomogeneous cases. By employing some techniques of real analysis, especially the method of a weight function, a new half-discrete Hi...