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＜電子ブック＞
Hardy Operators, Function Spaces and Embeddings / by David E. Edmunds, William D. Evans
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2004.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2004
本文言語	英語
大きさ	XII, 328 p : online resource
著者標目	*Edmunds, David E author Evans, William D author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Functions of real variables LCSH:Differential equations LCSH:Integral equations LCSH:Operator theory FREE:Functional Analysis FREE:Real Functions FREE:Differential Equations FREE:Integral Equations FREE:Operator Theory
一般注記	1 Preliminaries -- 2 Hardy-type Operators -- 3 Banach function spaces -- 4 Poincaré and Hardy inequalities -- 5 Generalised ridged domains -- 6 Approximation numbers of Sobolev embeddings -- References -- Author Index -- Notation Index 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. Of the many developments of the basic theory since its inception, two are of particular interest: (i) the consequences of working on space domains with irregular boundaries; (ii) the replacement of Lebesgue spaces by more general Banach function spaces. Both of these arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. These aspects of the theory will probably enjoy substantial further growth, but even now a connected account of those parts that have reached a degree of maturity 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. The significance of generalised ridged domains stems from their ability to 'unidimensionalise' the problems we study, reducing them to associated problems on trees or even on intervals. 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 HTTP:URL=https://doi.org/10.1007/978-3-662-07731-3

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