Tuomas Hytönen, Cornelia Kaiser

New Proof of the $T(1)$ Theorem for Triebel-Lizorkin Spaces

We give a new proof of the $T(1)$ theorem for reflexive homogeneous Triebel-Lizorkin spaces $\dot F^{s,q}_p$, which uses neither maximal functions nor atomic decompositions. The substitute tool is an estimate on translations in the $L_p(\ell_q)$ spaces.

Singular integral, translation operator, vector-valued estimate, Littlewood-Paley decomposition.

MSC 2000: Primary: 47G10. Secondary: 42B20, 47B38