Jonas Azzam

activity

20092025

most citedA new characterization of chord-arc domains

69 citations · 285 across the 26 of their papers we have counts for

collaborators

42 papers

math.CA2025

Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries

Jonas Azzam, Mihalis Mourgoglou, Michele Villa

Given a corkscrew domain with uniformly rectifiable boundary, we construct a surjective trace map onto the $L^{p}$ Hajlasz-Sobolev space on the boundary from the space of functions o…

math.CA2023

Quantitative differentiability on uniformly rectifiable sets

Jonas Azzam, Mihalis Mourgoglou, Michele Villa

We prove $L^{p}$ quantitative differentiability estimates for functions defined on uniformly rectifiable subsets of the Euclidean space. More precisely, we show that a Dorronsoro-typ…

math.CA2020★ 1 cited

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_…

math.CA2020

The weak lower density condition and uniform rectifiability

Jonas Azzam, Matthew Hyde

We show that an Ahlfors $d$ -regular set $E$ in $R^{n}$ is uniformly rectifiable if the set of pairs $(x, r) \in E \times (0, \infty)$ for which there exists $y \in B (x, r)$ and…

math.CA2019

Poincaré Inequalities and Uniform Rectifiability

Jonas Azzam

We show that any $d$ -Ahlfors regular subset of $R^{n}$ supporting a weak $(1, d)$ -Poincaré inequality with respect to surface measure is uniformly rectifiable.

math.CA2019★ 58 cited

Harmonic measure and quantitative connectivity: geometric characterization of the $L^{p}$ -solvability of the Dirichlet problem

Jonas Azzam, Steve Hofmann, José María Martell +2

It is well-known that quantitative, scale invariant absolute continuity (more precisely, the weak- $A_{\infty}$ property) of harmonic measure with respect to surface measure, on the b…