Equivalent Statements of Hilbert-Type Integral Inequalities
In this chapter, by the use of methods of real analysis and weight functions, we consider a few equivalent statements of Hilbert-type integral inequalities with a general nonhomogeneous kernel related to certain parameters. In the form of applications, a few equivalent statements of Hilbert-type integral inequalities with a general homogeneous kernel are deduced. Moreover, we also consider operator expressions, a few particular cases, and some examples related to the extended Hurwitz zeta function as applications.
- 1.Kuang, J.C.: Real and Functional Analysis (continuation) (sec. vol.). Higher Education Press, Beijing, China (2015)Google Scholar
- 2.Kuang, J.C.: Applied Inequalities. Shangdong Science and Technology Press, Jinan, China (2004)Google Scholar
- 3.Zhong, Y.Q.: Introduction to Complex Functions (Third Volume). Higher Education Press, Beijing (2003)Google Scholar
- 4.Wang, Z.X., Guo, D.R.: Introduction to Special Functions. Science Press, Beijing (1979)Google Scholar