Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers

Continuity envelopes for the spaces of generalised smoothness Bpq(s,Ψ)(ℝn) and Fpq(s,Ψ)(ℝn) are studied in the so-called supercritical s=1+n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept...

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Main Authors:	António M. Caetano, Dorothee D. Haroske
Format:	Article
Language:	English
Published:	Hindawi Limited 2005-01-01
Series:	Journal of Function Spaces and Applications
Online Access:	http://dx.doi.org/10.1155/2005/165785

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spelling	doaj-ec11bf1d2895426799798090864c59402020-11-25T01:04:40ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022005-01-0131337110.1155/2005/165785Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbersAntónio M. Caetano0Dorothee D. Haroske1Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, PortugalMathematical Institute, Friedrih-Shiller-University Jena, D-07737 Jena, GermanyContinuity envelopes for the spaces of generalised smoothness Bpq(s,Ψ)(ℝn) and Fpq(s,Ψ)(ℝn) are studied in the so-called supercritical s=1+n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some embeddings between function spaces to hold, as well as in the study of the asymptotic behaviour of approximation numbers of related embeddings.http://dx.doi.org/10.1155/2005/165785
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	António M. Caetano Dorothee D. Haroske
spellingShingle	António M. Caetano Dorothee D. Haroske Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers Journal of Function Spaces and Applications
author_facet	António M. Caetano Dorothee D. Haroske
author_sort	António M. Caetano
title	Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers
title_short	Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers
title_full	Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers
title_fullStr	Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers
title_full_unstemmed	Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers
title_sort	continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers
publisher	Hindawi Limited
series	Journal of Function Spaces and Applications
issn	0972-6802
publishDate	2005-01-01
description	Continuity envelopes for the spaces of generalised smoothness Bpq(s,Ψ)(ℝn) and Fpq(s,Ψ)(ℝn) are studied in the so-called supercritical s=1+n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some embeddings between function spaces to hold, as well as in the study of the asymptotic behaviour of approximation numbers of related embeddings.
url	http://dx.doi.org/10.1155/2005/165785
work_keys_str_mv	AT antoniomcaetano continuityenvelopesofspacesofgeneralisedsmoothnessalimitingcaseembeddingsandapproximationnumbers AT dorotheedharoske continuityenvelopesofspacesofgeneralisedsmoothnessalimitingcaseembeddingsandapproximationnumbers
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Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers

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