Hardy Operators, Function Spaces and Embeddings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XII, 328 p) |
| ISBN: | 9783662077313 9783642060274 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-07731-3 |
Internformat
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Datensatz im Suchindex
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| any_adam_object | |
| author | Edmunds, David E. |
| author_facet | Edmunds, David E. |
| author_role | aut |
| author_sort | Edmunds, David E. |
| author_variant | d e e de dee |
| building | Verbundindex |
| bvnumber | BV042423398 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-07731-3 |
| format | Electronic eBook |
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| id | DE-604.BV042423398 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662077313 9783642060274 |
| issn | 1439-7382 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858815 |
| oclc_num | 1165550945 |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 328 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Springer Monographs in Mathematics |
| spelling | Edmunds, David E. Verfasser aut Hardy Operators, Function Spaces and Embeddings by David E. Edmunds, W. Desmond Evans Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XII, 328 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 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 Mathematics Functional analysis Integral equations Operator theory Differential Equations Differential equations, partial Real Functions Ordinary Differential Equations Partial Differential Equations Integral Equations Functional Analysis Operator Theory Mathematik Banach-Raum (DE-588)4004402-6 gnd rswk-swf Integraloperator (DE-588)4131247-8 gnd rswk-swf Sobolev-Einbettung (DE-588)4181713-8 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Sobolev-Raum (DE-588)4055345-0 s Integraloperator (DE-588)4131247-8 s Sobolev-Einbettung (DE-588)4181713-8 s 1\p DE-604 Evans, W. Desmond Sonstige oth https://doi.org/10.1007/978-3-662-07731-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Edmunds, David E. Hardy Operators, Function Spaces and Embeddings Mathematics Functional analysis Integral equations Operator theory Differential Equations Differential equations, partial Real Functions Ordinary Differential Equations Partial Differential Equations Integral Equations Functional Analysis Operator Theory Mathematik Banach-Raum (DE-588)4004402-6 gnd Integraloperator (DE-588)4131247-8 gnd Sobolev-Einbettung (DE-588)4181713-8 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4131247-8 (DE-588)4181713-8 (DE-588)4055345-0 |
| title | Hardy Operators, Function Spaces and Embeddings |
| title_auth | Hardy Operators, Function Spaces and Embeddings |
| title_exact_search | Hardy Operators, Function Spaces and Embeddings |
| title_full | Hardy Operators, Function Spaces and Embeddings by David E. Edmunds, W. Desmond Evans |
| title_fullStr | Hardy Operators, Function Spaces and Embeddings by David E. Edmunds, W. Desmond Evans |
| title_full_unstemmed | Hardy Operators, Function Spaces and Embeddings by David E. Edmunds, W. Desmond Evans |
| title_short | Hardy Operators, Function Spaces and Embeddings |
| title_sort | hardy operators function spaces and embeddings |
| topic | Mathematics Functional analysis Integral equations Operator theory Differential Equations Differential equations, partial Real Functions Ordinary Differential Equations Partial Differential Equations Integral Equations Functional Analysis Operator Theory Mathematik Banach-Raum (DE-588)4004402-6 gnd Integraloperator (DE-588)4131247-8 gnd Sobolev-Einbettung (DE-588)4181713-8 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Mathematics Functional analysis Integral equations Operator theory Differential Equations Differential equations, partial Real Functions Ordinary Differential Equations Partial Differential Equations Integral Equations Functional Analysis Operator Theory Mathematik Banach-Raum Integraloperator Sobolev-Einbettung Sobolev-Raum |
| url | https://doi.org/10.1007/978-3-662-07731-3 |
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