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

Abstract

Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\Rd$ with weights $\W(x)= (1-|x|^2)^{μ-1/2}$, $\mu \ge 0$, 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 $\{\ip{f,ϕ_ξ}\}$ in appropriate sequence spaces.

30 pages

References in corpus (1)

• Maximal function and Multiplier Theorem for Weighted Space on the Unit Sphere