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arXiv · 2607.20206

Rough averages of triangular Hilbert transforms

Fred Yu-Hsiang Lin·Lenka Slavíková
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Abstract

We study a bilinear singular integral operator obtained by taking rough averages of certain directional variants of the triangular Hilbert transform. This operator can be interpreted as the twisted paraproduct with a rough homogeneous kernel. Under a balance condition on the $L^q$ integrability of the kernel on the unit sphere, we establish a range of $L^{p_1} \times L^{p_2} \rightarrow L^p$ bounds for this operator. Our results are optimal within the known boundedness range for the twisted paraproduct with a smooth kernel.

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Fred Yu-Hsiang Lin, Lenka Slavíková. 2026-07-22. Rough averages of triangular Hilbert transforms. https://arxiv.org/abs/2607.20206

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