Czechoslovak Mathematical Journal, Vol. 67, No. 2, pp. 497-513, 2017
Equivalent quasi-norms and atomic decomposition of weak Triebel-Lizorkin spaces
Wenchang Li, Jingshi Xu
Received January 26, 2016. First published May 16, 2017.
Abstract: 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.