Weighted Inequalities Of Hardy Type

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This is a survey 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 new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone function 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.