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.

中文翻译：

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Chebyshev阈值贪婪算法的Lebesgue不等式

在Banach空间中一般碱基的情况下，我们建立了Chebyshev弱阈值贪婪算法的Lebesgue参数的估计。这些概括并稍微改善了Dilworth等人的早期结果。（Rev Mat Complut 28（2）：393-409，2015），并辅以显示边界最优性的示例。我们的结果还阐明了邵和叶（J Inequal Appl 2018（1）：102，2018）中最近宣布的某些界限，并回答了该论文中尚待解决的一些问题。