Sharp lower bounds ||S_p(1_A)||_1 ≳ |A|* log(1/|A|*) are established for dyadic square functions S1 and S2 on indicators, using Brownian exit times and the Takagi function.
On the L p norms of stochastic integrals and other martingales , Duke Mathematical Jurnal Vol
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Sharp Lower Bounds for Dyadic Square Functions of indicator functions of sets
Sharp lower bounds ||S_p(1_A)||_1 ≳ |A|* log(1/|A|*) are established for dyadic square functions S1 and S2 on indicators, using Brownian exit times and the Takagi function.