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Abstract:

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.

Registro:

Documento: Artículo
Título:Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
Autor:Cabrelli, C.; Molter, U.; Romero, J.L.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Capital Federal, Argentina
IMAS, UBA-CONICET, Argentina
Palabras clave:Affine systems; Anisotropic function spaces; Besov spaces; Non-uniform atomic decomposition; Triebel-Lizorkin spaces
Año:2013
Volumen:232
Número:1
Página de inicio:98
Página de fin:120
DOI: http://dx.doi.org/10.1016/j.aim.2012.09.026
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00018708_v232_n1_p98_Cabrelli.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v232_n1_p98_Cabrelli

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Citas:

---------- APA ----------
Cabrelli, C., Molter, U. & Romero, J.L. (2013) . Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces. Advances in Mathematics, 232(1), 98-120.
http://dx.doi.org/10.1016/j.aim.2012.09.026
---------- CHICAGO ----------
Cabrelli, C., Molter, U., Romero, J.L. "Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces" . Advances in Mathematics 232, no. 1 (2013) : 98-120.
http://dx.doi.org/10.1016/j.aim.2012.09.026
---------- MLA ----------
Cabrelli, C., Molter, U., Romero, J.L. "Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces" . Advances in Mathematics, vol. 232, no. 1, 2013, pp. 98-120.
http://dx.doi.org/10.1016/j.aim.2012.09.026
---------- VANCOUVER ----------
Cabrelli, C., Molter, U., Romero, J.L. Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces. Adv. Math. 2013;232(1):98-120.
http://dx.doi.org/10.1016/j.aim.2012.09.026