92 citations · 502 across the 56 of their papers we have counts for
4 papers · 1 filter
On measures that improve dimension under convolution
Eino Rossi, Pablo Shmerkin
The dimensions, for , quantify the degree of smoothness of a measure. We study the following problem on the real line: when does the dimension improve under…
Improved bounds for the dimensions of planar distance sets
Pablo Shmerkin
We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of planar Borel sets of dimension slightly larger than , improving recent estimat…
Maximal Operators for cube skeletons
Andrea Olivo, Pablo Shmerkin
We study discretized maximal operators associated to averaging over (neighborhoods of) squares in the plane and, more generally, -skeletons in . Although these ope…
New bounds on the dimensions of planar distance sets
Tamás Keleti, Pablo Shmerkin
We prove new bounds on the dimensions of distance sets and pinned distance sets of planar sets. Among other results, we show that if is a Borel set of Hausdo…