Lebesgue inequalities for Chebyshev thresholding greedy algorithms

P. M. Berná, Blasco, G. Garrigós, E. Hernández, T. Oikhberg

Research output: Contribution to journalArticlepeer-review

Abstract

We establish estimates for the Lebesgue parameters of the Chebyshev weak thresholding greedy algorithm in the case of general bases in Banach spaces. These generalize and slightly improve earlier results in Dilworth et al. (Rev Mat Complut 28(2):393–409, 2015), and are complemented with examples showing the optimality of the bounds. Our results also clarify certain bounds recently announced in Shao and Ye (J Inequal Appl 2018(1):102, 2018), and answer some questions left open in that paper.

Original languageEnglish (US)
Pages (from-to)695-722
Number of pages28
JournalRevista Matematica Complutense
Volume33
Issue number3
DOIs
StatePublished - Sep 1 2020

Keywords

  • Quasi-greedy basis
  • Semi-greedy bases
  • Thresholding Chebyshev greedy algorithm
  • Thresholding greedy algorithm

ASJC Scopus subject areas

  • General Mathematics

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