Lebesgue inequalities for Chebyshev thresholding greedy algorithms

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

doi:10.1007/s13163-019-00328-9

Lebesgue inequalities for Chebyshev thresholding greedy algorithms

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

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	695-722
Number of pages	28
Journal	Revista Matematica Complutense
Volume	33
Issue number	3
DOIs	https://doi.org/10.1007/s13163-019-00328-9
State	Published - Sep 1 2020

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s13163-019-00328-9

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AU - Berná, P. M.

AU - Blasco,

AU - Garrigós, G.

AU - Hernández, E.

AU - Oikhberg, T.

PY - 2020/9/1

Y1 - 2020/9/1

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AB - 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.

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KW - Semi-greedy bases

KW - Thresholding Chebyshev greedy algorithm

KW - Thresholding greedy algorithm

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Lebesgue inequalities for Chebyshev thresholding greedy algorithms

Abstract

Keywords

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