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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