Weighted Inequalities Of Hardy Type: Second Edition

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 areas 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.

In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.

Readership: Postgraduates and researchers in mathematical analysis, engineering, numerical analysis and applied mathematics.

Reviews of the First Edition:

"The basic ideas are very well explained, the exposition is clear and the authors give complete proofs of most of the results they present." -- Mathematical Reviews

"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." -- SIAM Review

"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." -- Zentralblatt MATH