Lebesgue inequalities for Chebyshev thresholding greedy algorithms
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 sho...
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| Vydané v: | Revista matemática complutense Ročník 33; číslo 3; s. 695 - 722 |
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Springer International Publishing
01.09.2020
Springer Nature B.V |
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| 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. |
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| AbstractList | 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. 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. |
| Author | Berná, P. M. Hernández, E. Garrigós, G. Oikhberg, T. Blasco, Ó. |
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| Keywords | 41A46 46B15 41A65 Quasi-greedy basis Thresholding greedy algorithm Semi-greedy bases Thresholding Chebyshev greedy algorithm |
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| References | Ciesielski (CR7) 1968; 31 Konyagin, Temlyakov (CR15) 1999; 5 Temlyakov (CR24) 1998; 8 Berná (CR3) 2019; 417 Temlyakov, Yang, Ye (CR26) 2011; 17 Albiac, Ansorena (CR1) 2017; 30 CR17 Berná, Blasco, Garrigós (CR5) 2017; 30 Konyagin, Temlyakov (CR16) 2002; 28 Dilworth, Kutzarova, Oikhberg (CR10) 2015; 28 Berná, Blasco (CR4) 2017; 215 Garrigós, Hernández, Oikhberg (CR12) 2013; 38 Dilworth, Kalton, Kutzarova, Temlyakov (CR9) 2003; 19 Shao, Ye (CR19) 2018; 2018 Dilworth, Kalton, Kutzarova (CR8) 2003; 159 CR2 Katznelson (CR14) 1976 Ruckle (CR18) 1974; 26 Weisz (CR27) 2001; 146 Singer (CR21) 1981 Berná, Blasco, Garrigós, Hernández, Oikhberg (CR6) 2018; 48 Dovbysh, Nikolskii, Sudakov (CR11) 1986; 34 Temlyakov (CR23) 2011 Temlyakov, Tikhonov (CR25) 2015 Hajek, Montesinos Santalucía, Vanderwerff, Zizler (CR13) 2008 Wojtaszczyk (CR28) 2000; 107 Singer (CR20) 1970 Temlyakov (CR22) 1998; 14 I Singer (328_CR20) 1970 G Garrigós (328_CR12) 2013; 38 SJ Dilworth (328_CR9) 2003; 19 PM Berná (328_CR3) 2019; 417 I Singer (328_CR21) 1981 PM Berná (328_CR4) 2017; 215 C Shao (328_CR19) 2018; 2018 VN Temlyakov (328_CR26) 2011; 17 VN Temlyakov (328_CR22) 1998; 14 PM Berná (328_CR6) 2018; 48 P Hajek (328_CR13) 2008 SV Konyagin (328_CR15) 1999; 5 Z Ciesielski (328_CR7) 1968; 31 F Weisz (328_CR27) 2001; 146 SV Konyagin (328_CR16) 2002; 28 SJ Dilworth (328_CR10) 2015; 28 PM Berná (328_CR5) 2017; 30 328_CR17 F Albiac (328_CR1) 2017; 30 VN Temlyakov (328_CR24) 1998; 8 328_CR2 Y Katznelson (328_CR14) 1976 VN Temlyakov (328_CR23) 2011 P Wojtaszczyk (328_CR28) 2000; 107 WH Ruckle (328_CR18) 1974; 26 LN Dovbysh (328_CR11) 1986; 34 SJ Dilworth (328_CR8) 2003; 159 VN Temlyakov (328_CR25) 2015 |
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| SubjectTerms | Algebra Analysis Applications of Mathematics Banach spaces Chebyshev approximation Geometry Greedy algorithms Mathematics Mathematics and Statistics Parameter estimation Topology |
| Title | Lebesgue inequalities for Chebyshev thresholding greedy algorithms |
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