Restricted non-linear approximation in sequence spaces and applications to wavelet bases and interpolation
Entity
UAM. Departamento de MatemáticasPublisher
Springer VerlagDate
2013-01-01Citation
10.1007/s00605-012-0425-6
Monatshefte für Mathematik 169.2 (2013): 187-217
ISSN
0026-9255 (print); 1436-5081 (online)DOI
10.1007/s00605-012-0425-6Funded by
Research supported by GrantS MTM2007-60952 and MTM2010-16518 of SpainProject
Gobierno de España. MTM2007-60952; Gobierno de España. MTM2010-16518Editor's Version
http://dx.doi.org/10.1007/s00605-012-0425-6Subjects
Besov spaces; Democracy functions; Interpolation spaces; Lorentz spaces; Non-linear approximation; Triebel-Lizorkin spaces; MatemáticasNote
The final publication is available at Springer via http://dx.doi.org/10.1007/s00605-012-0425-6Rights
© Springer-Verlag 2012Abstract
Restricted non-linear approximation is a type of N-term approximation where a measure ν on the index set (rather than the counting measure) is used to control the number of terms in the approximation. We show that embeddings for restricted non-linear approximation spaces in terms of weighted Lorentz sequence spaces are equivalent to Jackson and Bernstein type inequalities, and also to the upper and lower Temlyakov property. As applications we obtain results for wavelet bases in Triebel–Lizorkin spaces by showing the Temlyakov property in this setting. Moreover, new interpolation results for Triebel–Lizorkin and Besov spaces are obtained
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Google Scholar:Hernández Rodríguez, Eugenio
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Vera, Daniel
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