Smooth and localized Riesz bases for L^2 spaces defined by Muchenhoupt weights

AIMAR HUGO; RAMOS WILFREDO

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2015 vol. 430 p. 417 - 427

0022-247X

Let $w$ be an $A_{infty}$-Muckenhoupt weight in $letra{R}$. Let $ L^{2}(wdx)$ denote the space of square integrable real functions  with the measure $w(x)dx$ and  the weighted scalar product $pin{f,g}_{w}=int_{letra{R}}fg~wdx$. By regularization of an unbalanced Haar system in $L^{2}(wdx)$ we construct absolutely continuous  Riesz bases with supports as close to the dyadic intervals as desired. Also  the Riesz bounds can be chosen  as close to $1$ as desired. The main tool used in the proof is Cotlar´s Lemma.