Kakeya maximal function
= Kakeya maximal function
{c}
{title2=$\mathcal K_\delta f(e)$}
For a direction $e$, the <Kakeya maximal function> is the supremum over translations of normalized averages of $|f|$ over unit-length <Kakeya tubes> in direction $e$. It measures how large a function can be on at least one thin tube in each direction. Normalizing by tube volume is essential when comparing different thicknesses.