D. Dkabrowski

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math.CA2025

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

Damian DÄ browski, Xavier Tolsa

In this work we provide a geometric characterization of the measures $I^¼$ in $R^{n + 1}$ with polynomial upper growth of degree $n$ such that the $n$ -dimensional Riesz transf…

math.CA2025

On the logarithmic equilibrium measure on curves

Damian DÄ browski, Tuomas Orponen

Let $I^¼$ be the logarithmic equilibrium measure on a compact set $I^^{3} \subset R^{d}$ . We prove that $I^¼$ is absolutely continuous with respect to the length measure on the p…

math.CA2024

Visible parts and slices of Ahlfors regular sets

Damian DÄ browski

We show that for any compact set $E \subset R^{d}$ the visible part of $E$ has Hausdorff dimension at most $d - 1/6$ for almost every direction. This improves recent estimates o…

The measures with L2-bounded Riesz transform and the PainlevÃ© problem

On the logarithmic equilibrium measure on curves

Visible parts and slices of Ahlfors regular sets

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