Bilinear Kakeya range conjecture

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Let n≥2n\geq2, let K∗(q′×q′→p′/2)K^*(q'\times q'\to p'/2) denote the bilinear adjoint estimate associated with the discretized x-ray transform, and let 1≤p,q≤∞1\leq p,q\leq\infty.

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

p≤n,p\leq n, n−2q+2p≥1.\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.

References

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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