69 citations · 285 across the 26 of their papers we have counts for
7 papers · 2 filters
Uniform rectifiability, elliptic measure, square functions, and -approximability via an ACF monotonicity formula
Jonas Azzam, John Garnett, Mihalis Mourgoglou +1
Let , , be an open set with Ahlfors-David regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator i…
Some remarks on the Lipschitz regularity of Radon transforms
Jonas Azzam, Jonathan Hickman, Sean Li
A set in the Euclidean plane is constructed whose image under the classical Radon transform is Lipschitz in every direction. It is also shown that, under mild hypotheses, for any s…
On a two-phase problem for harmonic measure in general domains
Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa +1
We show that, for disjoint domains in the Euclidean space, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rec…
An Analyst's Traveling Salesman Theorem for sets of dimension larger than one
Jonas Azzam, Raanan Schul
In his 1990 Inventiones paper, P. Jones characterized subsets of rectifiable curves in the plane via a multiscale sum of -numbers. These -numbers are geometric quantities mea…
The one-phase problem for harmonic measure in two-sided NTA domains
Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa
We show that if is a two-sided NTA domain with AD-regular boundary such that the logarithm of the Poisson kernel belongs to , where is th…
Absolute continuity of harmonic measure for domains with lower regular boundaries
Murat Akman, Jonas Azzam, Mihalis Mourgoglou
We study absolute continuity of harmonic measure with respect to surface measure on domains that have large complements. We show that if is -Ahlf…