Hardy Type Inequalities on Time Scales

Description

The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc.In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and the classical ones. To the best of the authors’ knowledge this is the first book devoted to Hardy-typeinequalities and their extensions on time scales. Front Matter....Pages i-x Hardy and Littlewood Type Inequalities....Pages 1-48 Copson-Type Inequalities....Pages 49-67 Leindler-Type Inequalities....Pages 69-89 Littlewood-Bennett Type Inequalities....Pages 91-120 Weighted Hardy Type Inequalities....Pages 121-151 Levinson-Type Inequalities....Pages 153-219 Hardy-Knopp Type Inequalities....Pages 221-294 Back Matter....Pages 295-305