An extrapolation theorem for nonlinear approximation and its applications

We prove an extrapolation theorem for the nonlinear m-term approximation with respect to a system of functions satisfying very mild conditions. This theorem allows us to prove endpoint Lp - Lq estimates in nonlinear approximation. As a consequence, some known endpoint estimates can be deduced directly and some new estimates are also obtained. Finally, applications of these new estimates are given to spherical m-widths and m-term approximation of the weighted Besov classes.

• Type: Journal
• Year: 2006
• Where: JAT
• Authors: Feng Dai
• Keywords: Endpoint Estimates, JAT 2006, M-term Approximation, Nonlinear M-term Approximation