Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces

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In this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces Lp(Rd), 1 < p < + ∞. The novelty and difficulty of this construction is that we allow for non-lattice translations.We prove that for...

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Autores principales:	Cabrelli, C., Molter, U., Romero, J.L.
Formato:	Artículo publishedVersion
Publicado:	2013
Materias:	Affine systems Anisotropic function spaces Besov spaces Non-uniform atomic decomposition Triebel-Lizorkin spaces
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00018708_v232_n1_p98_Cabrelli https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v232_n1_p98_Cabrelli_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_00018708_v232_n1_p98_Cabrelli_oai
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spelling	I28-R145-paper_00018708_v232_n1_p98_Cabrelli_oai2024-08-16 Cabrelli, C. Molter, U. Romero, J.L. 2013 In this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces Lp(Rd), 1 < p < + ∞. The novelty and difficulty of this construction is that we allow for non-lattice translations.We prove that for an arbitrary expansive matrix A and any set Λ-satisfying a certain spreadness condition but otherwise irregular-there exists a smooth window whose translations along the elements of Λ and dilations by powers of A provide an atomic decomposition for the whole range of the anisotropic Triebel-Lizorkin spaces. The generating window can be either chosen to be bandlimited or to have compact support.To derive these results we start with a known general "painless" construction that has recently appeared in the literature. We show that this construction extends to Besov and Triebel-Lizorkin spaces by providing adequate dual systems. © 2012 Elsevier Ltd. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Romero, J.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_00018708_v232_n1_p98_Cabrelli info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Adv. Math. 2013;232(1):98-120 Affine systems Anisotropic function spaces Besov spaces Non-uniform atomic decomposition Triebel-Lizorkin spaces Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v232_n1_p98_Cabrelli_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic	Affine systems Anisotropic function spaces Besov spaces Non-uniform atomic decomposition Triebel-Lizorkin spaces
spellingShingle	Affine systems Anisotropic function spaces Besov spaces Non-uniform atomic decomposition Triebel-Lizorkin spaces Cabrelli, C. Molter, U. Romero, J.L. Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
topic_facet	Affine systems Anisotropic function spaces Besov spaces Non-uniform atomic decomposition Triebel-Lizorkin spaces
description	In this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces Lp(Rd), 1 < p < + ∞. The novelty and difficulty of this construction is that we allow for non-lattice translations.We prove that for an arbitrary expansive matrix A and any set Λ-satisfying a certain spreadness condition but otherwise irregular-there exists a smooth window whose translations along the elements of Λ and dilations by powers of A provide an atomic decomposition for the whole range of the anisotropic Triebel-Lizorkin spaces. The generating window can be either chosen to be bandlimited or to have compact support.To derive these results we start with a known general "painless" construction that has recently appeared in the literature. We show that this construction extends to Besov and Triebel-Lizorkin spaces by providing adequate dual systems. © 2012 Elsevier Ltd.
format	Artículo Artículo publishedVersion
author	Cabrelli, C. Molter, U. Romero, J.L.
author_facet	Cabrelli, C. Molter, U. Romero, J.L.
author_sort	Cabrelli, C.
title	Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_short	Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_full	Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_fullStr	Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_full_unstemmed	Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_sort	non-uniform painless decompositions for anisotropic besov and triebel-lizorkin spaces
publishDate	2013
url	http://hdl.handle.net/20.500.12110/paper_00018708_v232_n1_p98_Cabrelli https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v232_n1_p98_Cabrelli_oai
work_keys_str_mv	AT cabrellic nonuniformpainlessdecompositionsforanisotropicbesovandtriebellizorkinspaces AT molteru nonuniformpainlessdecompositionsforanisotropicbesovandtriebellizorkinspaces AT romerojl nonuniformpainlessdecompositionsforanisotropicbesovandtriebellizorkinspaces
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Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces

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