Poincaré inequalities and Sobolev spaces

Our understsanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended...

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Detalles Bibliográficos
Autor: MacManus, Paul
Tipo de recurso: artículo
Fecha de publicación:2002
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:138525
Acceso en línea:https://ddd.uab.cat/record/138525
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_Esco02_08
Access Level:acceso abierto
Palabra clave:Poincaré inequalities
Sobolev inequalities
Metric spaces
Doubling measures
Descripción
Sumario:Our understsanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended to a wide variety of different settings. This paper reviews some of these new results and techniques and concludes with an example on the preservation of Sobolev spaces by the maximal function.