The characterizations of weighted sobolev spaces by wavelets and scaling functions

Mitsuo Izuki

doi:10.11650/twjm/1500405350

The characterizations of weighted sobolev spaces by wavelets and scaling functions

Mitsuo Izuki

Graduate School of Education

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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	Unknown Journal
Volume	13
Issue number	2 A
DOIs	https://doi.org/10.11650/twjm/1500405350
Publication status	Published - 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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10.11650/twjm/1500405350

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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.",

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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.

KW - A weight

KW - Greedy basis

KW - Scaling function

KW - Unconditional basis

KW - Wavelet

KW - Weighted sobolev space

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EP - 492

JO - Unknown Journal

JF - Unknown Journal

IS - 2 A

ER -

The characterizations of weighted sobolev spaces by wavelets and scaling functions

Abstract

Keywords

ASJC Scopus subject areas

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