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An L $^{3}$ bound for the trilinear Hilbert transform

Proves that the principal-value trilinear Hilbert transform with shifts

x-t

x-2t

x-3t

is bounded from

L^3(\mathbb R)^3

L^1(\mathbb R)

. This resolves the L

^{3}

exponent case of the standard conjecture for slopes 1, 2, 3.

Manuscripts in this family · 1

Oct 5, 2026·paper.pdf

We prove that the trilinear Hilbert transform with fixed slopes 1, 2, 3 maps

L^3(\mathbb R)\times L^3(\mathbb R)\times L^3(\mathbb R)

L^1(\mathbb R)

, resolving this case of the trilinear Hilbert transform conjecture.

Full abstract