2016, Hans Georg Feichtinger, Felix Voigtlaender, “From Frazier-Jawerth characterizations of Besov spaces to Wavelets and Decomposition spaces”, in arXiv[1]:
For Besov-Triebel-Lizorkin spaces, one uses a dyadic decomposition, while a uniform decomposition yields modulation spaces. Only recently, the second author has established a fruitful connection between modern variants of wavelet theory with respect to general dilation groups (which can be treated in the context of coorbit theory) and a particular family of decomposition spaces.
