Taiwanese Journal of Mathematics


Mitsuo Izuki

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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.

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

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

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]

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


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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