Lebesgue-type inequalities in greedy approximation
Functional Analysis
2019-10-01 v1
Abstract
We present new results regarding Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces. We improve earlier bounds in Temlyakov (Forum Math Sigma 2014), for dictionaries satisfying a new property introduced here. We apply these results to derive optimal bounds in two natural examples of sequence spaces. In particular, optimality is obtained in the case of the multivariate Haar system in Lp with 1<p<2, under the Littlewood-Paley norm.
Keywords
Cite
@article{arxiv.1909.13536,
title = {Lebesgue-type inequalities in greedy approximation},
author = {Stephen Dilworth and Gustavo Garrigos and Eugenio Hernandez and Denka Kutzarova and Vladimir Temlyakov},
journal= {arXiv preprint arXiv:1909.13536},
year = {2019}
}
Comments
33 pages, 1 figure