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What is the relation between the notion of singular integral operators and partial differential equations? I know, for example, that there is a relation between the Cauchy transform (Riesz transforms in higher dimension) and the laplacian, but it seems that this connection is much deeper. I want to know much more about that (I have a bite experince in harmonic analysis but not in PDE). Any suggested refrences (survey papers, etc) are welcome.

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