Pablo Shmerkin

activity

20042025

most citedLocal entropy averages and projections of fractal measures

92 citations · 502 across the 56 of their papers we have counts for

collaborators

Showing 2021Show all

5 papers · 1 filter

math.CA2021★ 1 cited

On the distance sets spanned by sets of dimension $d /2$ in $R^{d}$

Pablo Shmerkin, Hong Wang

We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient…

math.DS2021

On normal numbers and self-similar measures

Amir Algom, Simon Baker, Pablo Shmerkin

Let ${f_{i} (x) = s_{i} \cdot x + t_{i}}$ be a self-similar IFS on $R$ and let $β > 1$ be a Pisot number. We prove that if $\frac{l o g ∣ s _{i} ∣}{l o g β} \in / Q$ fo…

math.CA2021

Slices and distances: on two problems of Furstenberg and Falconer

Pablo Shmerkin

We survey the history and recent developments around two decades-old problems that continue to attract a great deal of interest: the slicing $\times 2$ , $\times 3$ conjecture of H.…

math.CA2021

New bounds on Cantor maximal operators

Pablo Shmerkin, Ville Suomala

We prove $L^{p}$ bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. Łaba and M. Pramanik a…

math.CA2021★ 1 cited

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane

Tuomas Orponen, Pablo Shmerkin

Let $0 \leq s \leq 1$ and $0 \leq t \leq 2$ . An $(s, t)$ -Furstenberg set is a set $K \subset R^{2}$ with the following property: there exists a line set $L$ of Ha…

On the distance sets spanned by sets of dimension d/2 in Rd

On normal numbers and self-similar measures

Slices and distances: on two problems of Furstenberg and Falconer

New bounds on Cantor maximal operators

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane

On the distance sets spanned by sets of dimension $d /2$ in $R^{d}$