Bilinear Kakeya range conjecture

Let n2n\geq2, let K(q×qp/2)K^*(q'\times q'\to p'/2) denote the bilinear adjoint estimate associated with the discretized x-ray transform, and let 1p,q1\leq p,q\leq\infty.

Bilinear Kakeya range conjecture. K(q×qp/2)K^*(q'\times q'\to p'/2) holds if and only if

pn,p\leq n, n2q+2p1.\frac{n-2}{q}+\frac{2}{p}\geq1.

The source presents this as equivalent to the Kakeya conjecture after interpolation and bilinearization. The source gives no resolution status.

Sources & referencesView supporting material

Primary source

Terence Tao, Ana Vargas and Luis Vega, “A bilinear approach to the restriction and Kakeya conjectures”, arXiv:math/9807163 (1998).

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