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Decomposition of weighted Triebel–Lizorkin and Besov spaces on the ball
Author(s) -
Kyriazis G.,
Petrushev P.,
Xu Yuan
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdn010
Subject(s) - mathematics , besov space , unit sphere , pure mathematics , ball (mathematics) , decomposition , decomposition theorem , polynomial , mathematical analysis , interpolation space , functional analysis , ecology , biochemistry , chemistry , biology , gene
Weighted Triebel–Lizorkin and Besov spaces on the unit ball B d in ℝ d with weights w μ ( 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 {〈 f , φ ξ 〉} in appropriate sequence spaces.