Hardy-type inequalities
Author(s)
Bibliographic Information
Hardy-type inequalities
（Pitman research notes in mathematics series, 219）
Longman Scientific & Technical , Wiley, 1990
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Kyoto Institute of Technology Library図
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Note
Bibliography: p. 327-333
Description and Table of Contents
Description
This provides a discussion of Hardy-type inequalities. They play an important role in various branches of analysis such as approximation theory, differential equations, theory of function spaces etc. The one-dimensional case is dealt with almost completely. Various approaches are described and some extensions are given (eg the case of estaimates involving higher order derivatives, or the dependence on the class of funcions for which the inequality should hold). The N-dimensional case is dealt with via the one-dimensional case as well as by using appropriate special approaches.
Table of Contents
- Part 1 The one-dimensional Hardy inequality on (a,b): historical remarks
- various methods of deriving it
- necessary and sufficient conditions for various classes of smooth functions u (u(a) = 0, or u(b) = 0, or u(a) = u(b) = 0). Part 2 The n-dimensional Hardy inequality: the approach via the one-dimensional case (special coordinates, special weights)
- the approach via differential equations (general weights)
- the approach via weighted norm inequalities (weights from the Muckenhoupt class AP)
- general necessary and sufficient conditions (the Maz'ja approach via capacities). Part 3 Weighted norm inequalities (a short survey of some special results). Part 4 Imbedding theorems for weighted Sobolev spaces: the Hardy inequality as an imbedding of a weighted Sobolev space into a weighted Lebesgue space
- the one-dimensional case
- the n-dimensional case
- special weights.
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