We characterize the Schauder and the unconditional basis properties for the Haar system in the Triebel–Lizorkin spaces \(F^s_{p,q}({{\mathbb {R}}}^d)\), at the endpoint cases \(s=1\), \(s=d/p-d\), and \(p=\infty \). Together with the earlier results in Garrigós et al. (J Fourier Anal Appl 24(5):1319–1339, 2018) and Seeger and Ullrich (Math Z 285:91–119, 2017), this completes the picture for such properties in the Triebel–Lizorkin scale, and complements a similar study for the Besov spaces given in Garrigós et al. (Basis properties of the Haar system in limiting Besov spaces. In: Geometric aspects of harmonic analysis: a conference in honour of Fulvio Ricci, Springer-INdAM series, arXiv.1901.09117).

在端点情况下，我们描述了Triebel–Lizorkin空间\（F ^ s_ {p，q}（{{\ mathbb {R}}} ^ d）\）中Haar系统的Schauder和无条件基础性质\ （s = 1 \），\（s = d / pd \）和\（p = \ infty \）。连同Garrigós等人的早期结果。（J Fourier Anal Appl 24（5）：1319–1339，2018）和Seeger and Ullrich（Math Z 285：91–119，2017），这完成了Triebel–Lizorkin量表中此类属性的图片，并补充了类似的内容Garrigós等人给出的Besov空间的研究。（限制Besov空间中Haar系统的基本性质。在：谐波分析的几何方面：纪念Fulvio Ricci的会议，Springer-INdAM系列，arXiv.1901.09117）。