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Lacey, Michael T.; Vähäkangas, Antti V.

On the local \(Tb\) theorem: a direct proof under the duality assumption. (English) Zbl 1343.42019

Proc. Edinb. Math. Soc., II. Ser. 59, No. 1, 193-222 (2016).
The authors present a new direct proof of a known local \(Tb\) theorem in the Euclidean setting. This proof avoids a reduction to the perfect dyadic case unlike some previous approaches [P. Auscher and X. Y. Qi, Publ. Mat., Barc. 53, No. 1, 179–196 (2009; Zbl 1153.42003)]. The important point is the use of random grids and the corresponding construction of the corona. The authors also apply certain twisted martingale transform inequalities.
Reviewer: Petr Gurka (Praha)

Cited in 2 Documents

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis
60G46 Martingales and classical analysis

Keywords:

local \(Tb\) theorem; \(T1\) theorem; corona; twisted martingale transform; stopping cubes

Citations:

Zbl 1153.42003
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References:

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