A Hilbert-type integral inequality in the whole plane related to the kernel of exponent function

Yanru Zhong; Meifa Huang; Bicheng Yang

doi:10.1186/s13660-018-1834-4

A Hilbert-type integral inequality in the whole plane related to the kernel of exponent function

J Inequal Appl. 2018;2018(1):234. doi: 10.1186/s13660-018-1834-4. Epub 2018 Sep 12.

Authors

Yanru Zhong¹, Meifa Huang², Bicheng Yang³

Affiliations

¹ 1School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin, P.R. China.
² 2School of Mechanical Science and Electrical Engineering, Guilin University of Electronic Technology, Guilin, P.R. China.
³ 3Department of Mathematics, Guangdong University of Education, Guangzhou, P.R. China.

Abstract

By using real analysis and weight functions, we obtain a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of exponent function with intermediate variables. The constant factor related to the gamma function is proved to be the best possible. We also consider some particular cases and the operator expressions.

Keywords: Equivalent statement; Gamma function; Hilbert-type integral inequality; Intermediate variable; Operator; Weight function.