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

Wenchang Li; Jingshi Xu

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 2, page 497-513
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Li, Wenchang, and Xu, Jingshi. "Equivalent quasi-norms and atomic decomposition of weak Triebel-Lizorkin spaces." Czechoslovak Mathematical Journal 67.2 (2017): 497-513. <http://eudml.org/doc/288178>.

@article{Li2017,
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.},
author = {Li, Wenchang, Xu, Jingshi},
journal = {Czechoslovak Mathematical Journal},
keywords = {weak Lebesgue space; Triebel-Lizorkin space; equivalent norm; maximal function; atom},
language = {eng},
number = {2},
pages = {497-513},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Equivalent quasi-norms and atomic decomposition of weak Triebel-Lizorkin spaces},
url = {http://eudml.org/doc/288178},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Li, Wenchang
AU - Xu, Jingshi
TI - Equivalent quasi-norms and atomic decomposition of weak Triebel-Lizorkin spaces
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 2
SP - 497
EP - 513
AB - 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.
LA - eng
KW - weak Lebesgue space; Triebel-Lizorkin space; equivalent norm; maximal function; atom
UR - http://eudml.org/doc/288178
ER -

References

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