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Morrey Spaces on Domains: Different Approaches and Growth Envelopes

We deal with Morrey spaces on bounded domains [Formula: see text] obtained by different approaches. In particular, we consider three settings [Formula: see text] , [Formula: see text] and [Formula: see text] , where [Formula: see text] , commonly used in the literature, and study their connections a...

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Autores principales: Haroske, Dorothee D., Schneider, Cornelia, Skrzypczak, Leszek
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6294180/
https://www.ncbi.nlm.nih.gov/pubmed/30839873
http://dx.doi.org/10.1007/s12220-017-9843-y
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author Haroske, Dorothee D.
Schneider, Cornelia
Skrzypczak, Leszek
author_facet Haroske, Dorothee D.
Schneider, Cornelia
Skrzypczak, Leszek
author_sort Haroske, Dorothee D.
collection PubMed
description We deal with Morrey spaces on bounded domains [Formula: see text] obtained by different approaches. In particular, we consider three settings [Formula: see text] , [Formula: see text] and [Formula: see text] , where [Formula: see text] , commonly used in the literature, and study their connections and diversities. Moreover, we determine the growth envelopes [Formula: see text] as well as [Formula: see text] , and obtain some applications in terms of optimal embeddings. Surprisingly, it turns out that the interplay between p and u in the sense of whether [Formula: see text] or [Formula: see text] plays a decisive role when it comes to the behaviour of these spaces.
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spelling pubmed-62941802018-12-28 Morrey Spaces on Domains: Different Approaches and Growth Envelopes Haroske, Dorothee D. Schneider, Cornelia Skrzypczak, Leszek J Geom Anal Article We deal with Morrey spaces on bounded domains [Formula: see text] obtained by different approaches. In particular, we consider three settings [Formula: see text] , [Formula: see text] and [Formula: see text] , where [Formula: see text] , commonly used in the literature, and study their connections and diversities. Moreover, we determine the growth envelopes [Formula: see text] as well as [Formula: see text] , and obtain some applications in terms of optimal embeddings. Surprisingly, it turns out that the interplay between p and u in the sense of whether [Formula: see text] or [Formula: see text] plays a decisive role when it comes to the behaviour of these spaces. Springer US 2017-04-24 2018 /pmc/articles/PMC6294180/ /pubmed/30839873 http://dx.doi.org/10.1007/s12220-017-9843-y Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Haroske, Dorothee D.
Schneider, Cornelia
Skrzypczak, Leszek
Morrey Spaces on Domains: Different Approaches and Growth Envelopes
title Morrey Spaces on Domains: Different Approaches and Growth Envelopes
title_full Morrey Spaces on Domains: Different Approaches and Growth Envelopes
title_fullStr Morrey Spaces on Domains: Different Approaches and Growth Envelopes
title_full_unstemmed Morrey Spaces on Domains: Different Approaches and Growth Envelopes
title_short Morrey Spaces on Domains: Different Approaches and Growth Envelopes
title_sort morrey spaces on domains: different approaches and growth envelopes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6294180/
https://www.ncbi.nlm.nih.gov/pubmed/30839873
http://dx.doi.org/10.1007/s12220-017-9843-y
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