Democracy functions and optimal embeddings for approximation spaces
Entity
UAM. Departamento de MatemáticasPublisher
Springer New York LLCDate
2012-08-01Citation
10.1007/s10444-011-9197-0
Advances in Computational Mathematics 37.2 (2012): 255-283
ISSN
1019-7168 (print); 1572-9044 (online)DOI
10.1007/s10444-011-9197-0Funded by
Research supported by Grant MTM2007-60952 of SpainProject
Gobierno de España. MTM2007-60952Editor's Version
http://dx.doi.org/10.1007/s10444-011-9197-0Subjects
Democratic bases; Discrete Lorentz spaces; Greedy algorithm; Jackson and Bernstein inequalities; Non-linear approximation; Wavelets; MatemáticasNote
The final publication is available at Springer via http://dx.doi.org/10.1007/s10444-011-9197-0Rights
© Springer Science+Business Media, LLC 2011Abstract
We prove optimal embeddings for nonlinear approximation spaces Aαq, in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for N-term wavelet approximation in L p , Orlicz, and Lorentz norms. We also study the “greedy classes” Gαq introduced by Gribonval and Nielsen, obtaining new counterexamples which show that Gαq≠Aαq for most non-democratic unconditional bases
Files in this item
Google Scholar:Garrigós, Gustavo
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Hernández Rodríguez, Eugenio
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de Natividade, Maria
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