A weak molecule condition is given for the Triebel-Lizorkin spaces Ḟ_p^{α,q}, with 0 < α < 1 and 1 < p, q < ∞. As an easy corollary, one may deduce, by atomic-molecular methods, a Triebel-Lizorkin space "T1" Theorem of Han and Sawyer, and Han, Jawerth, Taibleson and Weiss, for Calderón-Zygmund kernels K(x,y) which are not assumed to satisfy any regularity condition in the y variable.
@article{bwmeta1.element.bwnjournal-article-smv101i2p113bwm, author = {Steve Hofmann}, title = {A weak molecule condition for certain Triebel-Lizorkin spaces}, journal = {Studia Mathematica}, volume = {103}, year = {1992}, pages = {113-122}, zbl = {0811.46025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv101i2p113bwm} }
Hofmann, Steve. A weak molecule condition for certain Triebel-Lizorkin spaces. Studia Mathematica, Tome 103 (1992) pp. 113-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv101i2p113bwm/
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