Sparse T1 theorems

Abstract: Many operators in analysis are non-local, in the sense that a perturbation of the input near a point modifies the output everywhere; consider for example the operator that maps the initial data to the corresponding solution of the heat equation.

Sparse Domination consists in controlling such operators by a sum of positive, local averages. This allows to derive plenty of estimates, which are often optimal. For example, it has been shown that Calderón--Zygmund operators and square functions admit such a domination even under minimal $T1$ hypotheses.\newline

In this talk we introduce the concept of sparse domination and present a sparse $T1$ theorem for square functions, discussing the new difficulties and ideas in this case.

Time permitting, we will see how sparse domination can be applied in very different context.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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