Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane

  • Bicheng Yang Department of Mathematics, Guangdong University and of Education, Guangzhou, Guangdong 510303, P. R. China.
  • Dongmei Xin Department of Mathematics, Guangdong University and of Education, Guangzhou, Guangdong 510303, P. R. China.
  • Aizhen Wang Department of Mathematics, Guangdong University and of Education, Guangzhou, Guangdong 510303, P. R. China.
Keywords: Hilbert-type integral inequality, weight function, equivalent statement, operator, beta function

Abstract

By means of the technique of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related the beta function is proved to be the best possible. As applications, the case of the homogeneous kernel, the operator expressions and a few corollaries are considered.

Published
2020-06-16
How to Cite
Yang, B., Xin, D., & Wang, A. (2020). Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane. Recent Studies in Mathematics and Computer Science Vol. 2, 1-14. Retrieved from https://stm1.bookpi.org/index.php/rsmcs-v2/article/view/1448
Issue
Recent Studies in Mathematics and Computer Science Vol. 2
Section
Chapters