Kakeya inequality

Kakeya inequalities bound overlaps of long thin tubes with controlled directions.

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- Trilinear Kakeya inequality in three dimensions Kakeya inequality

Trilinear Kakeya inequality in three dimensions

For three transverse families of

R^{1/2} \times R^{1/2} \times R

tubes in

R^{3}

,

\prod_{j = 1}^{3} (\sum_{T \in T_{j}} χ_{T})^{1/3}_{3/2} ≲_{ϵ} R^{1 + ϵ} \prod_{j = 1}^{3} ∣ T_{j} ∣^{1/3} .

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