WEIGHTED INEQUALITIES OF HARDY TYPE
by Alois Kufner (Academy of Sciences, Czech Republic) & Lars-Erik Persson (Luleå University of Technology, Sweden)
Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy–Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman–Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.
Contents:
- Hardy's Inequality and Related Topics
- Some Weighted Norm
Inequalities
- The Hardy– Steklov Operator
- Higher Order Hardy Inequalities
- Fractional Order Hardy Inequalities
- Integral Operators on the Cone of Monotone Functions
Readership: Postgraduates and researchers in mathematical analysis,
engineering, numerical analysis and applied mathematics.
"The basic ideas are very well explained, the exposition is clear and the authors give complete proofs of most of the results they present."
“This book is very readable. There are informative endnotes in each chapter which give the history of and sometimes the connections to other theorems. The proofs are well planned and executed … I recommend this book to anyone interested in this kind of inequality or its applications.”
“This book is an excellent survey of the theory of weighted integral inequalities of Hardy type ... warmly recommended to researchers dealing with inequalities and related areas of mathematics.”
| Acta Scientiarum Mathematicarum |
“The basic ideas are very well written, the exposition is clear and the authors give complete proofs of most of the results they present.”
| 376pp |
Pub. date: Apr 2003 |
