61 citations · 237 across the 33 of their papers we have counts for
11 papers · 1 filter
Improved Cotlar's inequality in the context of local theorems
Henri Martikainen, Mihalis Mourgoglou, Xavier Tolsa
We prove in the context of local theorems with type testing conditions an improved version of Cotlar's inequality. This is related to the problem of removing the so call…
A new approach to non-homogeneous local theorems
Henri Martikainen, Mihalis Mourgoglou, Emil Vuorinen
We develop a new general method to prove various non-doubling local Tb theorems. The method combines the non-homogeneous good lambda method of Tolsa, the big pieces Tb theorem of N…
Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure
Jonas Azzam, Steve Hofmann, José María Martell +4
In the present paper we sketch the proof of the fact that for any open connected set , , and any with $0<\mathcal{H}^n(E)<\…
Harmonic measure and Riesz transform in uniform and general domains
Mihalis Mourgoglou, Xavier Tolsa
Let be open and let be some measure supported on such that for all , . We show that if…
Rectifiability of harmonic measure
Jonas Azzam, Steve Hofmann, José María Martell +4
In the present paper we prove that for any open connected set , , and any with , absolute continui…
Tangent measures and absolute continuity of harmonic measure
Jonas Azzam, Mihalis Mourgoglou
We show that for uniform domains whose boundaries satisfy a certain nondegeneracy condition that harmonic measure cannot be mutually absolutely contin…
Uniform domains with rectifiable boundaries and harmonic measure
Mihalis Mourgoglou
We assume that , , is a uniform domain with lower -Ahlfors-David regular and -rectifiable boundary. We show that if $\mathcal{H}^d|_{\par…
Rectifiability of harmonic measure in domains with porous boundaries
Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa
We show that if , is a connected domain with porous boundary, and is a set of finite and positive Hausdorff -measure…
Note about square function estimates and uniformly rectifiable measures
Henri Martikainen, Mihalis Mourgoglou
We generalise and offer a different proof of a recent square function estimate on UR sets by Hofmann, Mitrea, Mitrea and Morris. The proof is a short argument using the -n…
Singular sets for harmonic measure on locally flat domains with locally finite surface measure
Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa
A theorem of David and Jerison asserts that harmonic measure is absolutely continuous with respect to surface measure in NTA domains with Ahlfors regular boundaries. We prove that…
A characterization of -rectifiable doubling measures with connected supports
Jonas Azzam, Mihalis Mourgoglou
Garnett, Killip, and Schul have exhibited a doubling measure with support equal to which is -rectifiable, meaning there are countably many curves of…