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Hardy Operators, Function Spaces and Embeddings

Name: Hardy Operators, Function Spaces and Embeddings
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783642060274
Price: 19305 HUF
Availability: InStock

Szerző: William D. Evans

Nyelv:

Kötés: Puha kötésű

Kiadó: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Elérhetőség: Beszállítói készleten

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Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are...

Információk a könyvről

Szerző

William D. Evans

Nyelv

Angol

Kötés

Könyv - Puha kötésű

Kiadva

2011

oldal

328

EAN

9783642060274

ISBN

9783642060274

Enbook ID

06616922

Kiadó

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Súly

484

Méretek

157 x 232 x 18

Teljes leírás

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. 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.

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Hardy Operators, Function Spaces and Embeddings

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