Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 497–513

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

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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 

MSC 2010

46E35 42B25 42B35 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsHainan Normal UniversityHaikou, Hainan ProvincePeople’s Republic of China

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