= Kakeya maximal conjecture
{c}
{title2=$\|\mathcal K_\delta f\|_n\lesssim_{n,\varepsilon}\delta^{-\varepsilon}\|f\|_n$}
The maximal estimate used in the classical <Kakeya set> problem asks, for every $\varepsilon>0$, for a bound from $L^n(\mathbb R^n)$ to $L^n(S^{n-1})$ with loss at most $\delta^{-\varepsilon}$. Constants may depend on dimension and $\varepsilon$, but not tube thickness or the function. Applied to an <indicator function> of a neighborhood of a <Kakeya set>, it gives the <Kakeya Minkowski dimension conjecture>.
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