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

摘要

This paper deals with atomic decompositions in spaces of type (B{sub}(p,q)){sup}s(R{sup}n, w), (F{sub}(p,q)){sup}s (R{sup}n, w), 0 < p < ∞, 0 < q ≤ ∞, s ∈ R, where the weight function w belongs to some Muckenhoupt class A{sub}r. In particular, we consider the weight function (w{sub}κ){sup}Γ(x) = dist(x, Γ){sup}κ, where Γ is some d-set, 0 < d < n, and κ > -(n - d).