| Abstract: |
| A classical problem at the intersection of harmonic analysis and PDE is the boundedness of the so-called Calderon commutators, which, not being of convolution type, require creative tools to analyze. Indeed, we will see a new approach to these pioneered by C. Muscalu in 2014 through shifted variants of certain square and maximal functions, which have gone on to become rather fashionable tools in the last decade, especially in the theory of multilinear singular integrals. We will see in the context of some recent results on multilinear Fourier multipliers how these shifted operators naturally appear. Then, we will conclude by briefly investigating how these results can be applied to prove boundedness for a general class of rough multilinear singular integrals, which include the Calderon commutators as a special case. |
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