On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets

Detalhes bibliográficos
Autor(a) principal: Carvalho, A.
Data de Publicação: 2011
Outros Autores: Caetano, A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/5559
Resumo: The Hausdorff dimension of the graphs of the functions in Hölder and Besov spaces (in this case with integrability p≥1) on fractal d-sets is studied. Denoting by s in (0,1] the smoothness parameter, the sharp upper bound min{d+1-s, d/s} is obtained. In particular, when passing from d≥s to d<s there is a change of behaviour from d+1-s to d/s which implies that even highly nonsmooth functions defined on cubes in ℝn have not so rough graphs when restricted to, say, rarefied fractals. © 2011 Springer Science+Business Media, LLC.
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spelling On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-SetsBesov spacesBox counting dimensionContinuous functionsd-SetsFractalsHausdorff dimensionHölder spacesWaveletsWeierstrass functionThe Hausdorff dimension of the graphs of the functions in Hölder and Besov spaces (in this case with integrability p≥1) on fractal d-sets is studied. Denoting by s in (0,1] the smoothness parameter, the sharp upper bound min{d+1-s, d/s} is obtained. In particular, when passing from d≥s to d<s there is a change of behaviour from d+1-s to d/s which implies that even highly nonsmooth functions defined on cubes in ℝn have not so rough graphs when restricted to, say, rarefied fractals. © 2011 Springer Science+Business Media, LLC.Springer2012-01-27T16:45:18Z2011-01-01T00:00:00Z2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/5559eng1069-5869Carvalho, A.Caetano, A.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:07:04Zoai:ria.ua.pt:10773/5559Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:43:07.258382Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
title On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
spellingShingle On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
Carvalho, A.
Besov spaces
Box counting dimension
Continuous functions
d-Sets
Fractals
Hausdorff dimension
Hölder spaces
Wavelets
Weierstrass function
title_short On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
title_full On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
title_fullStr On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
title_full_unstemmed On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
title_sort On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
author Carvalho, A.
author_facet Carvalho, A.
Caetano, A.
author_role author
author2 Caetano, A.
author2_role author
dc.contributor.author.fl_str_mv Carvalho, A.
Caetano, A.
dc.subject.por.fl_str_mv Besov spaces
Box counting dimension
Continuous functions
d-Sets
Fractals
Hausdorff dimension
Hölder spaces
Wavelets
Weierstrass function
topic Besov spaces
Box counting dimension
Continuous functions
d-Sets
Fractals
Hausdorff dimension
Hölder spaces
Wavelets
Weierstrass function
description The Hausdorff dimension of the graphs of the functions in Hölder and Besov spaces (in this case with integrability p≥1) on fractal d-sets is studied. Denoting by s in (0,1] the smoothness parameter, the sharp upper bound min{d+1-s, d/s} is obtained. In particular, when passing from d≥s to d<s there is a change of behaviour from d+1-s to d/s which implies that even highly nonsmooth functions defined on cubes in ℝn have not so rough graphs when restricted to, say, rarefied fractals. © 2011 Springer Science+Business Media, LLC.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-01T00:00:00Z
2011
2012-01-27T16:45:18Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/5559
url http://hdl.handle.net/10773/5559
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1069-5869
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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