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 language | English |
|---|---|
| Pages (from-to) | 467-492 |
| Number of pages | 26 |
| Journal | Unknown Journal |
| Volume | 13 |
| Issue number | 2 A |
| DOIs | |
| Publication status | Published - Jan 1 2009 |
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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Izuki, M. (2009). The characterizations of weighted sobolev spaces by wavelets and scaling functions. Unknown Journal, 13(2 A), 467-492. https://doi.org/10.11650/twjm/1500405350