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arXiv · 1610.01531

The Sparse T1 Theorem

Michael T. Lacey·Darío Mena
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Abstract

We impose standard $ T1 $-type assumptions on a Calder\'on-Zygmund operator $ T $, and deduce that for bounded compactly supported functions $ f, g $ there is a sparse bilinear form $ \Lambda $ so that $$ \lvert \langle T f, g \rangle\rvert \lesssim \Lambda (f,g). $$ The proof is short and elementary. The sparse bound quickly implies all the standard mapping properties of a Calder\'on-Zygmund on a (weighted) $ L ^{p}$ space.

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Michael T. Lacey, Darío Mena. 2016-10-05. The Sparse T1 Theorem. https://arxiv.org/abs/1610.01531

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