Georgian Mathematical Journal 13 (2006), No. 3, 485--493
Copyright Heldermann Verlag 2006
New Proof of the T(1) Theorem for Triebel-Lizorkin Spaces
Tuomas Hytönen
Dept. of Mathematics, University of Turku, 20014 Turku, Finland
tuomas.hytonen@utu.fi
Cornelia Kaiser
Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, 76128 Karlsruhe, Germany
cornelia.kaiser@math.uni-karlsruhe.de
[Abstract-pdf]
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: 47G10; 42B20, 47B38
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