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

En:

Adv. Math. 2013;232(1):98-120

Fecha:

2013

Formato:

application/pdf

Tipo de documento:

info:eu-repo/semantics/article
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion

Descriptores:

Affine systems -  Anisotropic function spaces -  Besov spaces -  Non-uniform atomic decomposition -  Triebel-Lizorkin spaces

Descripción:

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.

Identificador(es):

http://hdl.handle.net/20.500.12110/paper_00018708_v232_n1_p98_Cabrelli

Derechos:

info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar