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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.
Sample Chapter(s)
Introduction (207 KB)
Chapter 1: Hardy's Inequality and Related Topics (1,215 KB)
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.
