The characterizations of weighted sobolev spaces by wavelets and scaling functions

Mitsuo Izuki

The characterizations of weighted sobolev spaces by wavelets and scaling functions

Mitsuo Izuki

Research output: Contribution to journal › Article

Abstract

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

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Izuki, M. (2009). The characterizations of weighted sobolev spaces by wavelets and scaling functions. Taiwanese Journal of Mathematics, 13(2 A), 467-492.

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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.

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KW - Scaling function

KW - Unconditional basis

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The characterizations of weighted sobolev spaces by wavelets and scaling functions

Abstract

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Keywords

ASJC Scopus subject areas

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