Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball

Kyriazis, G.; Petrushev, P.; Xu, Yuan

Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball

Authors

Kyriazis, G.

Petrushev, P.

Xu, Yuan

Description

Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\Rd$ with weights $\W(x)= (1-|x|^2)^{μ-1/2}$, $μ\ge 0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) $\{ϕ_ξ\}$, $\{ψ_ξ\}$ and it is shown that the membership of a distribution to the weighted Triebel-Lizorkin or Besov spaces can be determined by the size of the needlet coefficients $\{\ip{f,ϕ_ξ}\}$ in appropriate sequence spaces.
30 pages