An extrapolation theorem for nonlinear approximation and its applications |
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Authors: | Feng Dai |
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Institution: | aDepartment of Mathematical and Statistical Sciences, University of Alberta, CAB 632, Edmonton, Alta., Canada T6G 2G1 |
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Abstract: | 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. |
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Keywords: | Nonlinear m-term approximation Extrapolation Spherical widths Weighted Besov classes |
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