Wavelet bases in the weighted Besov and Triebel–Lizorkin spaces with Aploc-weights

doi:10.1016/j.jat.2008.12.003

Journal of Approximation Theory

Volume 161, Issue 2, December 2009, Pages 656-673

https://doi.org/10.1016/j.jat.2008.12.003 Get rights and content

Under an Elsevier user license

open archive

Abstract

We obtain wavelet characterizations of Besov spaces and the Triebel–Lizorkin spaces associated with $A_{\infty}^{loc}$ -weights. These characterizations are used to show that our wavelet bases are also greedy.

Keywords

Besov space

Triebel–Lizorkin space

Wavelet

Unconditional basis

Greedy basis