Taiwanese Journal of Mathematics

THE CHARACTERIZATIONS OF WEIGHTED SOBOLEV SPACES BY WAVELETS AND SCALING FUNCTIONS

Mitsuo Izuki

Full-text: Open access

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 $A_p^{\mathop{\mathrm{loc}}}$ weights. In the case of $w \in A_p$, we use only wavelets with proper regularity. Meanwhile, if we assume $w \in A_p^{\mathop{\mathrm{loc}}}$, 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.

Article information

Source
Taiwanese J. Math., Volume 13, Number 2A (2009), 467-492.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405350

Digital Object Identifier
doi:10.11650/twjm/1500405350

Mathematical Reviews number (MathSciNet)
MR2500001

Zentralblatt MATH identifier
1174.42044

Subjects
Primary: 42C40: Wavelets and other special systems 42B35: Function spaces arising in harmonic analysis 42C15: General harmonic expansions, frames 46B15: Summability and bases [See also 46A35]

Keywords
$A_p$ weight $A_p^{\mathop{\mathrm{loc}}}$ weight wavelet scaling function weighted Sobolev space unconditional basis greedy basis

Citation

Izuki, Mitsuo. THE CHARACTERIZATIONS OF WEIGHTED SOBOLEV SPACES BY WAVELETS AND SCALING FUNCTIONS. Taiwanese J. Math. 13 (2009), no. 2A, 467--492. doi:10.11650/twjm/1500405350. https://projecteuclid.org/euclid.twjm/1500405350


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