Parameterized Multidimensional Hilbert-Type Inequalities
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. In this book, applying the weight functions, the transfer formula, the parameterized idea and the technique of real analysis and functional analysis, we introduce multi-parameters and provide three kinds of multidimensional Hilbert-type inequalities with the general nonnegative measurable kernels and the best possible constant factors related to the Gamma function. The equivalent forms, the reverses and some Hardy-type inequalities are obtained. Furthermore, we consider the operator expressions with the norm, some particular inequalities and a large number of examples. The theory of multidimensional Hilbert-type inequalities and the operator expressions are built in this book. The lemmas and theorems provide an extensive account of these kinds of inequalities and operators.
Sample Chapter(s)
Preface (50 KB)
Components of the Book:
  • Head Page
  • Copyright
  • Foreword
  • Preface
  • Acknowledgments
  • Contents
  • Chapter 1. Introduction
  • Chapter 2. Multidimensional Hilbert-Type Integral Inequalities
  • Chapter 3. Multidimensional Discrete Hilbert-Type Inequalities and Their Operator Expression
  • Chapter 4. Multidimensional Half-Discrete Hilbert-Type Inequalities
  • References
Readership: Readers who are interested in Parameterized Multidimensional Hilbert-Type Inequalities
1
Head Page
Bicheng Yang, Jianquan Liao
Abstract | PDF (85 KB)
2
Copyright
Bicheng Yang, Jianquan Liao
Abstract | PDF (110 KB)
3
Foreword
Bicheng Yang, Jianquan Liao
Abstract | PDF (48 KB)
4
Preface
Bicheng Yang, Jianquan Liao
Abstract | PDF (50 KB)
5
Acknowledgments
Bicheng Yang, Jianquan Liao
Abstract | PDF (41 KB)
6
Contents
Bicheng Yang, Jianquan Liao
Abstract | PDF (71 KB)
1
Chapter 1. Introduction
Bicheng Yang, Jianquan Liao
Abstract | PDF (142 KB)
13
Chapter 2. Multidimensional Hilbert-Type Integral Inequalities
Bicheng Yang, Jianquan Liao
Abstract | PDF (602 KB)
85
Chapter 3. Multidimensional Discrete Hilbert-Type Inequalities and Their Operator Expression
Bicheng Yang, Jianquan Liao
Abstract | PDF (670 KB)
181
Chapter 4. Multidimensional Half-Discrete Hilbert-Type Inequalities
Bicheng Yang, Jianquan Liao
Abstract | PDF (0 KB)
259
References
Bicheng Yang, Jianquan Liao
Abstract | PDF (80 KB)
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, Associate professor,Department of Mathematics, Guangdong University of Education, Guangzhou, China.

Free SCIRP Newsletters
Add your e-mail address to receive free newsletters from SCIRP.
Copyright © 2006-2021 Scientific Research Publishing Inc. All Rights Reserved.
Top