The characterizations of weighted sobolev spaces by wavelets and scaling functions

Mitsuo Izuki

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3 Citations (Scopus)

Abstract

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
Volume13
Issue number2 A
Publication statusPublished - 2009
Externally publishedYes

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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