article

Title: Sharp Jackson and Bernstein inequalities for $N$-term approximation in sequence spaces with applications

Authors: Gustavo Garrigos and Eugenio Hernandez

Issue: Volume 53 (2004), Issue 6, 1741-1764

Abstract:

We study $N$-term approximation for general families of sequence spaces, establishing sharp versions of Jackson and Bernstein inequalities. The sequence spaces used are adapted to provide characterizations of Triebel-Lizorkin and Besov spaces by means of wavelet-like systems using general dilation matrices, and thus they include spaces of anisotropic smoothness. As an application, we characterize the $N$-term approximation spaces when the error is measured in the first of the spaces mentioned above.