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 | Taiwanese Journal of Mathematics |
| Volume | 13 |
| Issue number | 2 A |
| Publication status | Published - 2009 |
| Externally published | Yes |
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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)
Cite this
The characterizations of weighted sobolev spaces by wavelets and scaling functions. / Izuki, Mitsuo.
In: Taiwanese Journal of Mathematics, Vol. 13, No. 2 A, 2009, p. 467-492.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The characterizations of weighted sobolev spaces by wavelets and scaling functions
AU - Izuki, Mitsuo
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - A weight
KW - A weight
KW - Greedy basis
KW - Scaling function
KW - Unconditional basis
KW - Wavelet
KW - Weighted sobolev space
UR - http://www.scopus.com/inward/record.url?scp=74049162486&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=74049162486&partnerID=8YFLogxK
M3 - Article
VL - 13
SP - 467
EP - 492
JO - Taiwanese Journal of Mathematics
JF - Taiwanese Journal of Mathematics
SN - 1027-5487
IS - 2 A
ER -