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

• Autores: Cabrelli, C.; Molter, U.; Romero, J.L.
• Año de publicación: 2013
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Adv. Math. 2013;232(1):98-120
• Materia: Affine systems; Anisotropic function spaces; Besov spaces; Non-uniform atomic decomposition; Triebel-Lizorkin spaces
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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.