Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis

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ENTROPY AND APPROXIMATION NUMBERS OF EMBEDDINGS OF FUNCTION SPACES WITH MUCKENHOUPT WEIGHTS, II. GENERAL WEIGHTS (2011, methodology): “For later use we recall a ‘fractal’ example studied in [16].”
Entropy and Approximation Numbers of Embeddings of Function Spaces with Muckenhoupt Weights, I (2008, methodology): “[15, 31, 32] and Bownik [1, 2]. We partly rely on our approach [ 18 ].”
Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases (2011, background): “The well-definedness of it is immediate from the atomic decomposition characterisation of F s p,q(R, w), w ∈ A∞, in [24], since supp(1 − ψ)f ∩ B(0, 2) = ∅ such that”