Averages of simplex Hilbert transforms

Durcik, Polona; Roos, Joris

doi:10.1090/proc/15196

Averages of simplex Hilbert transforms
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by Polona Durcik and Joris Roos PDF

Proc. Amer. Math. Soc. 149 (2021), 633-647 Request permission

Abstract:

We study a multilinear singular integral obtained by taking averages of simplex Hilbert transforms. This multilinear form is also closely related to Calderón commutators and the twisted paraproduct. We prove $L^p$ bounds in dimensions two and three and give a conditional result valid in all dimensions.

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