The main theme of the book is the study, from the standpoint of
s-numbers, of integral operators of Hardy type and related Sobolev
embeddings. In the theory of s-numbers the idea is to attach to
every bounded linear map between Banach spaces a monotone
decreasing sequence of non-negative numbers with a view to the
classification of operators according to the way in which these
numbers approach a limit: approximation numbers provide an
especially important example of such numbers. The asymptotic
behavior of the s-numbers of Hardy operators acting between
Lebesgue spaces is determined here in a wide variety of cases. The
proof methods involve the geometry of Banach spaces and generalized
trigonometric functions; there are connections with the theory of
the p-Laplacian.
General
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