Abstract: | Weighted Triebel–Lizorkin and Besov spaces on the unitball Bd in d with weights wµ(x)=(1–|x|2)µ–1/2,µ0, are introduced and explored. A decomposition schemeis developed in terms of almost exponentially localized polynomialelements (needlets) {}, {} and it is shown that the membershipof a distribution to the weighted Triebel–Lizorkin orBesov spaces can be determined by the size of the needlet coefficients{f, } in appropriate sequence spaces. |