TY - JOUR
T1 - The characterizations of weighted sobolev spaces by wavelets and scaling functions
AU - Izuki, Mitsuo
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
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
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U2 - 10.11650/twjm/1500405350
DO - 10.11650/twjm/1500405350
M3 - Article
AN - SCOPUS:74049162486
VL - 13
SP - 467
EP - 492
JO - [No source information available]
JF - [No source information available]
SN - 0402-1215
IS - 2 A
ER -