On the Local Tb Theorem under Minimal Integrability

2012/06/13 by Lacey, Michael T, Vähäkangas, Antti V
#42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary: 42B20 Secondary: 42B25

paper · doi:10.48550/arxiv.1206.2861

Abstract

We prove a version of the local Tb Theorem assuming that the accretive functions b_Q and T b_Q are locally L ^p integrable, for any 1< p < ∞ . This improves a recent result of Hytonen-Nazarov. The proof strategy relies upon the their strategy, with additional techniques concerning twisted martingale differences and the use of random dyadic grids in the local Tb setting.

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