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We prove a range of Lp bounds for singular Brascamp-Lieb forms with cubical structure. We pass through sparse and local bounds, the latter proved by an iteration of Fourier expansion, telescoping, and the Cauchy-Schwarz inequality. We allow 2m−1 < p with m the dimension of the cube, extending an earlier result that required p = 2m. The threshold 2m−1 is sharp in our theorems.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Mathematische Zeitschrift in 2022 following peer review. The final publication may differ and is available at Springer via

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