D. Dkabrowski

activity

20212025

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math.CA2024

On the dimension of $s$ -Nikodým sets

Damian Dąbrowski, Max Goering, Tuomas Orponen

Let $s \in [0, 1]$ . We show that a Borel set $N \subset R^{2}$ whose every point is linearly accessible by an $s$ -dimensional family of lines has Hausdorff dimension at mos…

math.CA2024

The measures with $L^{2}$ -bounded Riesz transform and the Painlevé problem

Damian Dąbrowski, Xavier Tolsa

In this work we provide a geometric characterization of the measures $μ$ in $R^{n + 1}$ with polynomial upper growth of degree $n$ such that the $n$ -dimensional Riesz transfo…

On the dimension of s-Nikodým sets

The measures with L2-bounded Riesz transform and the Painlevé problem

On the dimension of $s$ -Nikodým sets

The measures with $L^{2}$ -bounded Riesz transform and the Painlevé problem