An extrapolation theorem for nonlinear approximation and its applications

摘要

We prove an extrapolation theorem for the nonlinear in-term approximation with respect to a system of functions satisfying very mild conditions. This theorem allows us to prove endpoint L-p- L-q 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 in-widths and in-term approximation of the weighted Besov classes. (c) 2006 Elsevier Inc. All rights reserved.