Work

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

Year: 2023

Type: article

Abstract: 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 non-homogeneous cases. By employing some techniques of real analysis, especially the way of weight function, a new half-discrete Hilbert-type inequality with the new kernel function, as well as its equivalent Hardy-type inequalities are established. Moreover, it is proved that the constant factors of the newly obtained inequalities are the best possible. Lastly, assigning special values to the parameters, some new half-discrete Hilbert-type inequalities with special kernels are presented at the end of the paper. 2020 Mathematics Subject Classification: Primary 26D15, 26D10; Secondary 47B38.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-023-02951-z

Author: Minghui You

Institution: Zhejiang Institute of Mechanical and Electrical Engineering

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,890

Funder: Department of Education of Zhejiang Province