A. Jonsson has constructed wavelets of higher order on self-similar sets, and characterized Besov spaces on totally disconnected self-similar sets, by means of the magnitude of the coefficients in the wavelet expansion of the function. For a class of self-similar sets, W. Jin shows that such wavelets can be constructed by recursively calculating moments. We extend their results to a class of graph-directed self-similar sets, introduced by R. D. Mauldin and S. C. Williams.
"Wavelets and Besov spaces on Mauldin-Williams fractals.." Real Anal. Exchange 32 (1) 119 - 144, 2006/2007.