In this book, by applying the weight functions, the idea of introduced parameters, the transfer formula, the Euler-Maclaurin summation formula and the techniques of real analysis and functional analysis, we use the well known Hardy’s integral inequalities to provide two kinds of extended applications on multidimensional half-discrete Hilbert-type inequalities, involving partial sum, derivative function of higher-order, multiple upper limit function and multiple lower limit function et al., as well as the equivalent statements and the cases of reverses, which mostly published by the journals in recent about ten years.
Sample Chapter(s)
Preface (62 KB)
Components of the Book:
- Chapter 1. Introduction: Research on the Theory of Hilbert-Type Inequalities and Applications
- Chapter 2. Extended Hardy-Hilbert's Inequalities Involving One Partial Sum
- Chapter 3. Extended More Accurate Hardy-Hilbert's Inequalities Involving One Partial Sum
- Chapter 4. Extended More Accurate Mulholland-Type Inequalities Involving One Partial Sum
- Chapter 5. Extended Hardy-Hilbert's Inequalities Involving One Multiple Upper Limit Function
- Chapter 6. Extended Hardy-Hilbert's Inequalities Involving One Derivative Function of m-Order
- Chapter 7. Extended Hilbert-Type Inequalities with the General Homogeneous Kernel Involving One Derivative Function of m-Order
- Chapter 8. Extended Hilbert-Type Inequalities with the General homogeneous Kernel and One Multiple Lower Limit Function
- Chapter 9. Extended Hilbert-Type Inequalities with the General Nonhomogeneous Kernel Involving One Derivative Function of m-Order
- Chapter 10. Extended Hilbert-Type Inequalities with the General Nonhomogeneous Kernel and One Multiple Lower Limit Function
- References
Readership:
Students, academics, teachers and other people attending or interested in extended applications on multidimensional half-discrete hilbert-type inequalities.
Bicheng Yang, Guangdong University of Education
male, he was born in August 1946 in the urban area of Shanwei City, Guangdong Province, China. He was appointed Professor of Mathematics in 1998. Now, he is the Director of the Institute of Applied Mathematics of Guangdong University of Education, and the Ph.D. supervisor of the University Utara Malaysia. He has been devoted to basic and applied research on Summability, Operator Theory, and Analytic Inequalities for a long time.
Jianquan Liao