Best m-term approximation and Lizorkin–Triebel spaces

• DOI: 10.1016/j.jat.2011.02.006
• Publication Date: 2011-02-18T09:44:55Z
• Authors: Markus Hansen; Winfried Sickel
• Keywords: Decay of wavelet coefficients; Lizorkin–Triebel spaces; Real interpolation; Besov spaces; Approximation spaces; Best m-term approximation; Wavelets; 0101 mathematics; 01 natural sciences

AbstractWe shall investigate the asymptotic behaviour of the widths of best m-term approximation with respect to Lizorkin–Triebel as well as Besov spaces. Our approach leads to final assertions in all possible situations. Furthermore, we shall also discuss embeddings into the approximation spaces Aqs(Lp) with q<∞. This leads to detailed information on the decay of wavelet coefficients for the elements of Lizorkin–Triebel and Besov spaces.