Artículos de revistas
Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
Fecha
2013-01-15Registro en:
Cabrelli, Carlos; Molter, Ursula Maria; Romero, Jose Luis Fernando; Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces; Elsevier; Advances in Mathematics; 232; 1; 15-1-2013; 98-120
0001-8708
Autor
Cabrelli, Carlos
Molter, Ursula Maria
Romero, Jose Luis Fernando
Resumen
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.