Lebesgue-type inequalities in greedy approximation

30 Sep 2019  ·  Dilworth Stephen, Garrigos Gustavo, Hernandez Eugenio, Kutzarova Denka, Temlyakov Vladimir ·

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.

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Functional Analysis
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