New bounds on Cantor maximal operators

We prove $L^p$ bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our improve upon those obtained by I. Łaba and M. Pramanik in some cases are sharp up endpoint. A consequence our main result is that there exist Salem Cantor sets any dimension $>1/2$ such operator bounded on $L^2(\mathbb{R})$. follow overall scheme Łaba-Pramanik analytic part argument, while probabilistic instead inspired earlier work intersection properties random measures.