Hardy Operators, Function Spaces and Embeddings

David Eric Edmunds, William D. Evans - Collection Springer Monographs in Mathematics

326 pages, parution le 09/08/2004

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Résumé

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains. This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.

Written for:
Researchers and graduate students in mathematical analysis, function spaces, integral operators, and differential operators

Sommaire

Preliminaries
Hardy-type Operators
Banach function spaces
Poincare and Hardy inequalities
Generalised ridged domains
Approximation numbers of Sobolev embeddings

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	David Eric Edmunds, William D. Evans
Collection	Springer Monographs in Mathematics
Parution	09/08/2004
Nb. de pages	326
Format	16 x 24
Couverture	Relié
Poids	630g
Intérieur	Noir et Blanc
EAN13	9783540219729