On the equivalence of brushlet and wavelet bases ✩

We prove that the Meyer wavelet basis and a class of brushlet systems associated with exponential type partitions of the frequency axis form a family of equivalent (unconditional) bases for the Besov and Triebel–Lizorkin function spaces. This equivalence is then used to obtain new results on nonlinear approximation with brushlets in Triebel–Lizorkin spaces.  2004 Elsevier Inc. All rights reserved.