Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces

Autores
Aimar, Hugo Alejandro; Bernardis, Ana Lucia; Martín Reyes, Francisco Javier
Año de publicación
2003
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study boundedness and convergence on Lp(ℝn, dμ) of the projection operators Pj given by MRA structures with non-necessarily compactly supported scaling function. As a consequence, we prove that if w is a locally integrable function such that w -1/p-1 (x)(1+|x|)-N is integrable for some N > 0, then the Muckenhoupt Ap condition is necessary and sufficient for the associated wavelet system to be an unconditional basis for the weighted space L p(ℝn, w(x) dx), 1 < p < ∞.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Martín Reyes, Francisco Javier. Universidad de Málaga; España
Materia
AP WEIGHTS
WAVELETS
WEIGHTED LEBESGUE SPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/100605
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/100605
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Multiresolution Approximations and Wavelet Bases of Weighted Lp SpacesAimar, Hugo AlejandroBernardis, Ana LuciaMartín Reyes, Francisco JavierAP WEIGHTSWAVELETSWEIGHTED LEBESGUE SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study boundedness and convergence on Lp(ℝn, dμ) of the projection operators Pj given by MRA structures with non-necessarily compactly supported scaling function. As a consequence, we prove that if w is a locally integrable function such that w -1/p-1 (x)(1+|x|)-N is integrable for some N > 0, then the Muckenhoupt Ap condition is necessary and sufficient for the associated wavelet system to be an unconditional basis for the weighted space L p(ℝn, w(x) dx), 1 < p < ∞.Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Martín Reyes, Francisco Javier. Universidad de Málaga; EspañaBirkhauser Boston Inc2003-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/100605Aimar, Hugo Alejandro; Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 9; 5; 3-2003; 497-5101069-5869CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-003-0024-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-26T09:08:20Zoai:ri.conicet.gov.ar:11336/100605instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-26 09:08:20.571CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
title Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
spellingShingle Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
Aimar, Hugo Alejandro
AP WEIGHTS
WAVELETS
WEIGHTED LEBESGUE SPACES
title_short Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
title_full Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
title_fullStr Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
title_full_unstemmed Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
title_sort Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces
dc.creator.none.fl_str_mv Aimar, Hugo Alejandro
Bernardis, Ana Lucia
Martín Reyes, Francisco Javier
author Aimar, Hugo Alejandro
author_facet Aimar, Hugo Alejandro
Bernardis, Ana Lucia
Martín Reyes, Francisco Javier
author_role author
author2 Bernardis, Ana Lucia
Martín Reyes, Francisco Javier
author2_role author
author
dc.subject.none.fl_str_mv AP WEIGHTS
WAVELETS
WEIGHTED LEBESGUE SPACES
topic AP WEIGHTS
WAVELETS
WEIGHTED LEBESGUE SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study boundedness and convergence on Lp(ℝn, dμ) of the projection operators Pj given by MRA structures with non-necessarily compactly supported scaling function. As a consequence, we prove that if w is a locally integrable function such that w -1/p-1 (x)(1+|x|)-N is integrable for some N > 0, then the Muckenhoupt Ap condition is necessary and sufficient for the associated wavelet system to be an unconditional basis for the weighted space L p(ℝn, w(x) dx), 1 < p < ∞.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Martín Reyes, Francisco Javier. Universidad de Málaga; España
description We study boundedness and convergence on Lp(ℝn, dμ) of the projection operators Pj given by MRA structures with non-necessarily compactly supported scaling function. As a consequence, we prove that if w is a locally integrable function such that w -1/p-1 (x)(1+|x|)-N is integrable for some N > 0, then the Muckenhoupt Ap condition is necessary and sufficient for the associated wavelet system to be an unconditional basis for the weighted space L p(ℝn, w(x) dx), 1 < p < ∞.
publishDate 2003
dc.date.none.fl_str_mv 2003-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/100605
Aimar, Hugo Alejandro; Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 9; 5; 3-2003; 497-510
1069-5869
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100605
identifier_str_mv Aimar, Hugo Alejandro; Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Multiresolution Approximations and Wavelet Bases of Weighted Lp Spaces; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 9; 5; 3-2003; 497-510
1069-5869
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-003-0024-y
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Birkhauser Boston Inc
publisher.none.fl_str_mv Birkhauser Boston Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.011256

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