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.
Durcik, P., Slavíková, L. & Thiele, C. Local bounds for singular Brascamp–Lieb forms with cubical structure. Math. Z. (2022). https://doi.org/10.1007/s00209-022-03148-8
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