Jonas Azzam

activity

20152019

most citedRectifiability of harmonic measure in domains with porous boundaries

6 citations · 6 across the 1 of their papers we have counts for

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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

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…

math.CA2019

Harmonic Measure and the Analyst's Traveling Salesman Theorem

Jonas Azzam

We study how generalized Jones $β$ -numbers relate to harmonic measure. Firstly, we generalize a result of Garnett, Mourgoglou and Tolsa by showing that domains in $\mathbb{R}^{d+1}…

math.CA2018

Dimension drop for harmonic measure on Ahlfors regular boundaries

Jonas Azzam

We show that given a domain $Ω \subseteq R^{d + 1}$ with uniformly non-flat Ahlfors $s$ -regular boundary and $s \geq d$ , the dimension of its harmonic measure is strictly less…

math.CA2018

Characterization of rectifiable measures in terms of $α$ -numbers

Jonas Azzam, Xavier Tolsa, Tatiana Toro

We characterize Radon measures $μ$ in $R^{n}$ that are $d$ -rectifiable in the sense that their supports are covered up to $μ$ -measure zero by countably many $d$ -dimensiona…

math.CA2015★ 6 cited

Rectifiability of harmonic measure in domains with porous boundaries

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

We show that if $n \geq 1$ , $Ω \subset R^{n + 1}$ is a connected domain with porous boundary, and $E \subset \partial Ω$ is a set of finite and positive Hausdorff $H^{n}$ -measure…

Poincaré Inequalities and Uniform Rectifiability

Harmonic measure and quantitative connectivity: geometric characterization of the Lp-solvability of the Dirichlet problem

Harmonic Measure and the Analyst's Traveling Salesman Theorem

Dimension drop for harmonic measure on Ahlfors regular boundaries

Characterization of rectifiable measures in terms of α-numbers

Rectifiability of harmonic measure in domains with porous boundaries

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

Characterization of rectifiable measures in terms of $α$ -numbers