The characterizations of weighted sobolev spaces by wavelets and scaling functions

Mitsuo Izuki

Research output: Contribution to journalArticle

3 Citations (Scopus)


We prove that suitable wavelets and scaling functions give characterizations and unconditional bases of the weighted Sobolev space Lp,s(w) with Ap or Alocp weights. In the case of w ∈ Ap, we use only wavelets with proper regularity. Meanwhile, if we assume w ∈ Alocp, not only compactly supported Cs+1-wavelets but also compactly supported Cs+1-scaling functions come into play. We also establish that our bases are greedy for Lp,s(w) after normalization.

Original languageEnglish
Pages (from-to)467-492
Number of pages26
JournalTaiwanese Journal of Mathematics
Issue number2 A
Publication statusPublished - 2009
Externally publishedYes



  • A weight
  • A weight
  • Greedy basis
  • Scaling function
  • Unconditional basis
  • Wavelet
  • Weighted sobolev space

ASJC Scopus subject areas

  • Mathematics(all)

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