Hilbert-type inequalities include Hilbert's inequalities, Hardy-Hilbert-type inequalities and Yang-Hilbert-type inequalities, which are important in Analysis and its applications. They are mainly divided three kinds of integral, discrete and half-discrete. In recent twenty years, there are many advances in research on Hilbert-type inequalities, especially in Yang-Hilbert-type inequalities.
In this book, by using the way of weight functions, the parameterized idea and technique of Real and Functional Analysis, we introduce multi-parameters and provide three kinds of double Hilbert-type inequalities with the general measurable kernels and the best possible constant factors. The equivalent forms, the reverses and some particular inequalities are obtained. Furthermore, the operator expressions with the norm, a large number of examples on the norm, some composition formulas of the operators, and three kinds of compositional inequalities with the best possible constant factors are considered. The theory of double Hilbert-type inequalities and operators are almost built. The lemmas and theorems provide an extensive account of these kinds of inequalities and operators.
Sample Chapter(s)
Preface (48 KB)
Components of the Book:
- Head Page
- Copyright
- Preface
- Acknowledgements
- Contents
- Chapter 1.Introduction: A Survey on the Study of Hilbert-Type Inequalities
- Chapter 2.The Case That the Kernels Are Related to Integral
- Chapter 3.The Case That the Kernels AreDiscrete
- Chapter 4.The Case That the Kernels Are Half-Discrete
- Chapter 5.Some Extensions of Hilbert-Type Inequalities
- References
Readership:
Students, academics, teachers and other people attending or interested in Hilbert-Type Inequalities
Bicheng Yang
Bicheng Yang, Hilbert-type inequalities including Hilbert's inequalities, Hardy-Hilbert-type inequalities and Yang-Hilbert-type inequalities are important in analysis and its applications, which are mainly divided into three classes of integral, discrete and half-discrete. In the last twenty years, there have been many advances in research on Hilbert-type inequalities, especially in Yang-Hilbert-type inequalities.
Jianquan Liao
Jianquan Liao, Associate professor，Department of Mathematics, Guangdong University of Education, Guangzhou, China.