Tuomas Hytönen, Cornelia Kaiser
Abstract:
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.
Keywords:
Singular integral, translation operator, vector-valued estimate,
Littlewood-Paley decomposition.
MSC 2000: Primary: 47G10. Secondary: 42B20, 47B38