On pointwise domination of Calderon-Zygmund operators by sparse operators

Mon, 30/05/2016 - 14:00
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Abstract: 

In this talk we survey several recent results establishing a pointwise domination of Calder\'on-Zygmund 
operators by sparse operators defined by
$${\mathcal A}_{\mathcal S}f(x)=\sum_{Q\in {\mathcal S}}\Big(\frac{1}{|Q|}\int_Qf\Big)\chi_{Q}(x),$$
where ${\mathcal S}$ is a sparse family of cubes from ${\mathbb R}^n$.
In particular, we present a simple proof of M. Lacey's theorem about Calder\'on-Zygmund operators
with Dini-continuous kernels in its quantitative form obtained by T. Hyt\"onen-L. Roncal-O. Tapiola.