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arXiv · 2307.05692

Lower Estimate on Square Function of an Indicator Set

Christina Giannitsi·Michael T. Lacey
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Abstract

Let $Sf$ be a discrete martingale square function. Then, for any set $V$ of positive probability, we have $\mathbb{E} S(\mathbf{1}_V)^2 \geq η\mathbb{P}(V)$ for an absolute constant $η>0$. We extend this to wavelet square functions, and discuss some related open questions.

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Christina Giannitsi, Michael T. Lacey. 2023-07-11. Lower Estimate on Square Function of an Indicator Set. https://arxiv.org/abs/2307.05692

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