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

G. Kyriazis·P. Petrushev·Yuan Xu
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Abstract

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.

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G. Kyriazis, P. Petrushev, Yuan Xu. 2007-03-14. Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball. https://arxiv.org/abs/math/0703403

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