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

A 2007 Preprint by G. Kyriazis, P. Petrushev, and Y. Xu

• 2007:05
• Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $R^d$ with weights $w _ \mu(x)=(1-|x|^2)^{\mu-\frac{1}{2}},$ $\mu\geq0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) $\{\varphi _ \xi\},\{\psi _ \xi\}$ 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 $\{\langle{f},\varphi _ \xi\rangle\}$ in appropriate sequence spaces.

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