Lebesgue-type inequalities in greedy approximation

S. Dilworth, G. Garrigós, E. Hernández, D. Kutzarova, V. Temlyakov

Research output: Contribution to journalArticlepeer-review


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 [19] 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.

Original languageEnglish (US)
Article number108885
JournalJournal of Functional Analysis
Issue number5
StatePublished - Mar 1 2021


  • Non-linear approximation
  • Thresholding greedy algorithm
  • Uniformly smooth Banach space
  • Weak Chebyshev greedy algorithm

ASJC Scopus subject areas

  • Analysis


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