Maximal operators for cube skeletons

Andrea Olivo, Pablo Shmerkin
2020 Annales Academiae Scientiarum Fennicae: Mathematica  
We study discretized maximal operators associated to averaging over (neighborhoods of) squares in the plane and, more generally, k-skeletons in R n . Although these operators are known not to be bounded on any L p , we obtain nearly sharp L p bounds for every small discretization scale. These results are motivated by, and partially extend, recent results of Keleti, Nagy and Shmerkin, and of Thornton, on sets that contain a scaled k-sekeleton of the unit cube with center in every point of R n .
doi:10.5186/aasfm.2020.4513 fatcat:cflmuhzuunfulfgbtvpfuupxke