1 citations · 1 across the 5 of their papers we have counts for
6 papers
On the logarithmic equilibrium measure on curves
Damian Dąbrowski, Tuomas Orponen
Let be the logarithmic equilibrium measure on a compact set . We prove that is absolutely continuous with respect to the length measure on the part…
On the dimension of -Nikodým sets
Damian Dąbrowski, Max Goering, Tuomas Orponen
Let . We show that a Borel set whose every point is linearly accessible by an -dimensional family of lines has Hausdorff dimension at mos…
The measures with -bounded Riesz transform and the Painlevé problem
Damian Dąbrowski, Xavier Tolsa
In this work we provide a geometric characterization of the measures in with polynomial upper growth of degree such that the -dimensional Riesz transfo…
Visible parts and slices of Ahlfors regular sets
Damian Dąbrowski
We show that for any compact set the visible part of has Hausdorff dimension at most for almost every direction. This improves recent estimates o…
Analytic capacity and dimension of sets with plenty of big projections
Damian Dąbrowski, Michele Villa
Our main result marks progress on an old conjecture of Vitushkin. We show that a compact set in the plane with plenty of big projections (PBP) has positive analytic capacity, along…
The measures with -bounded Riesz transform satisfying a subcritical Wolff-type energy condition
Damian Dąbrowski, Xavier Tolsa
In this work we obtain a geometric characterization of the measures in with polynomial upper growth of degree such that the -dimensional Riesz transfo…