Lebesgue-Type Inequalities for Quasi-greedy Bases

Gustavo Garrigós, Eugenio Hernández, Timur Oikhberg

Research output: Contribution to journalArticlepeer-review


We show that, for quasi-greedy bases in real or complex Banach spaces, an optimal bound for the ratio between greedy N-term approximation ∥x-G N x∥ and the best N-term approximation σ N(x) is controlled by max{μ(N),k N}, where μ(N) and k N are well-known constants that quantify the democracy and conditionality of the basis. In particular, for democratic bases this bound is O(logN). We show with various examples that these bounds are actually attained.

Original languageEnglish (US)
Pages (from-to)447-470
Number of pages24
JournalConstructive Approximation
Issue number3
StatePublished - Dec 2013


  • Bounded variation
  • Democracy functions
  • Lebesgue-type inequalities
  • Non-linear approximation
  • Quasi-greedy bases
  • Thresholding greedy algorithm

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics


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