2011/08/12 by Eugenio Hernández, Hernández, Eugenio, Daniel Vera +1
Mathematics · #41A17 #41C40 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1108.2610
openalex publication_date 2011/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Restricted non-linear approximation is a type of N-term approximation where a\nmeasure \ν on the index set (rather than the counting measure) is used to\ncontrol the number of terms in the approximation. We show that embeddings for\nrestricted non-linear approximation spaces in terms of weighted Lorentz\nsequence spaces are equivalent to Jackson and Bernstein type inequalities, and\nalso to the upper and lower Temlyakov property. As applications we obtain\nresults for wavelet bases in Triebel-Lizorkin spaces by showing the Temlyakow\nproperty in this setting. Moreover, new interpolation results for\nTriebel-Lizorkin and Besov spaces are obtained.\n