Damian Dąbrowski

activity

20172023

most citedStructure of sets with nearly maximal Favard length

5 citations · 6 across the 3 of their papers we have counts for

collaborators

11 papers

math.CA2023

How much can heavy lines cover?

Damian Dąbrowski, Tuomas Orponen, Hong Wang

One formulation of Marstrand's slicing theorem is the following. Assume that $t \in (1, 2]$ , and $B \subset R^{2}$ is a Borel set with $H^{t} (B) < \infty$ . Then,…

math.CA2022★ 1 cited

Quantitative Besicovitch projection theorem for irregular sets of directions

Damian Dąbrowski

The classical Besicovitch projection theorem states that if a planar set $E$ with finite length is purely unrectifiable, then almost all orthogonal projections of $E$ have zero len…

math.CA2022★ 5 cited

Structure of sets with nearly maximal Favard length

Alan Chang, Damian Dąbrowski, Tuomas Orponen +1

Let $E \subset B (1) \subset R^{2}$ be an $H^{1}$ measurable set with $H^{1} (E) < \infty$ , and let $L \subset R^{2}$ be a line segment with $\mat…

math.CA2021

Integrability of orthogonal projections, and applications to Furstenberg sets

Damian Dąbrowski, Tuomas Orponen, Michele Villa

Let $G (d, n)$ be the Grassmannian manifold of $n$ -dimensional subspaces of $R^{d}$ , and let $π_{V} : R^{d} \to V$ be the orthogonal projection. We p…

math.CA2020

Two examples related to conical energies

Damian Dąbrowski

In a recent article we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big…

math.CA2020

An $α$ -number characterization of $L^{p}$ spaces on uniformly rectifiable sets

Jonas Azzam, Damian Dąbrowski

We give a characterization of $L^{p} (σ)$ for uniformly rectifiable measures $σ$ using Tolsa's $α$ -numbers, by showing, for $1 < p < \infty$ and $f \in L^{p} (σ)$ , that \[ \lVert f\rVert_…

How much can heavy lines cover?

Quantitative Besicovitch projection theorem for irregular sets of directions

Structure of sets with nearly maximal Favard length

Integrability of orthogonal projections, and applications to Furstenberg sets

Two examples related to conical energies

An α-number characterization of Lp spaces on uniformly rectifiable sets

An $α$ -number characterization of $L^{p}$ spaces on uniformly rectifiable sets