Equivalent quasi-norms and atomic decomposition of weak Triebel-Lizorkin spaces

Li, Wenchang ; Xu, Jingshi

Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 497-513

Abstract (VO)

Recently, the weak Triebel-Lizorkin space was introduced by Grafakos and He, which includes the standard Triebel-Lizorkin space as a subset. The latter has a wide applications in aspects of analysis. In this paper, the authors firstly give equivalent quasi-norms of weak Triebel-Lizorkin spaces in terms of Peetre's maximal functions. As an application of those equivalent quasi-norms, an atomic decomposition of weak Triebel-Lizorkin spaces is given.

Détail

DOI : 10.21136/CMJ.2017.0037-16

Classification : 42B25, 42B35, 46E35
Keywords: weak Lebesgue space; Triebel-Lizorkin space; equivalent norm; maximal function; atom

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