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arXiv · 1510.01069

On a trilinear singular integral form with determinantal kernel

Philip Gressman·Danqing He·Vjekoslav Kovač·Brian Street·Christoph Thiele·Po-Lam Yung
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Abstract

We study a trilinear singular integral form acting on two-dimensional functions and possessing invariances under arbitrary matrix dilations and linear modulations. One part of the motivation for introducing it lies in its large symmetry groups acting on the Fourier side. Another part of the motivation is that this form stands between the bilinear Hilbert transforms and the first Calderón commutator, in the sense that it can be reduced to a superposition of the former, while it also successfully encodes the latter. As the main result we determine the exact range of exponents in which the ${L}^p$ estimates hold for the considered form.

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Philip Gressman, Danqing He, Vjekoslav Kovač, Brian Street, Christoph Thiele, Po-Lam Yung. 2015-10-05. On a trilinear singular integral form with determinantal kernel. https://doi.org/10.1090/proc%2F13007

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