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

2007/03/14 by George Kyriazis, Kyriazis, G., Pencho Petrushev +3 · 1 citation
Mathematics · #41A25 #42B35 #42C15 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.math/0703403

openalex publication_date 2007/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ 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 \\ipf,ϕ_ξ\ in appropriate sequence spaces.

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