A weak molecule condition for certain Triebel-Lizorkin spaces

Volume 101 / 1992

Steve Hofmann Studia Mathematica 101 (1992), 113-122 DOI: 10.4064/sm-101-2-113-122


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.


  • Steve Hofmann

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