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 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.

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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
• New and Complementary Results

Readership: Postgraduates and researchers in mathematical analysis, engineering, numerical analysis and applied mathematics.
Weighted Lebesque Spaces;Hardy's Inequality;Hardy-Type Operators;Hardyâ?"Steklov Operator;Duality Principle;Convexity;Scales of Characterizing Conditions0