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Can optimal rearrangement invariant Sobolev imbeddings be further extended?

Opened Access Can optimal rearrangement invariant Sobolev imbeddings be further extended?

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Autor: Curbera Costello, Guillermo
Ricker, Werner J.
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2007
Publicado en: Indiana University Mathematics Journal, 56 (3), 1479-1497.
Tipo de documento: Artículo
Resumen: Sobolev imbeddings (over suitable open subsets of Rn) can be extended from the classical Lp-setting to that of more general norms (required to be rearrangement invariant) on the underlying function spaces. This has been thoroughly studied in recent years and shown to be intimately connected to an associated kernel operator (of one variable). This kernel operator always has an optimal domain (being a Banach function space, but typically not rearrangement invariant) to which it can be continuously extended. So, techniques aside, there is no a priori reason not to treat Sobolev imbeddings for non-rearrangement invariant norms. This is the aim of the present paper.
Cita: Curbera Costello, G. y Ricker, W.J. (2007). Can optimal rearrangement invariant Sobolev imbeddings be further extended?. Indiana University Mathematics Journal, 56 (3), 1479-1497.
Tamaño: 283.8Kb
Formato: PDF

URI: http://hdl.handle.net/11441/41795

DOI: http://dx.doi.org/10.1512/iumj.2007.56.2929

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