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.
Keywords:  weak Lebesgue space; Triebel-Lizorkin space; equivalent norm; maximal function; atom
Classification MSC:  46E35, 42B25, 42B35
DOI:  10.21136/CMJ.2017.0037-16


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Affiliations:   Wenchang Li, Jingshi Xu, Department of Mathematics, Hainan Normal University, 99 Longkunnanlu, Haikou, Hainan Province, 571158, People's Republic of China, e-mail: 875666986@qq.com, jingshixu@126.com

 
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