J. M. Martell

activity

20062026

most citedSharp weighted estimates for classical operators

170 citations · 1.4k across the 61 of their papers we have counts for

collaborators

Showing 2015Show all

8 papers · 1 filter

math.CA2015★ 32 cited

The weak- $A_{\infty}$ property of harmonic and $p$ -harmonic measures implies uniform rectifiability

Steve Hofmann, Phi Le, José María Martell +1

Let $E \subset R^{n + 1}$ , $n \geq 2$ , be an Ahlfors-David regular set of dimension $n$ . We show that the weak- $A_{\infty}$ property of harmonic measure, for the open set $Ω:= \m…

math.CA2015★ 18 cited

On the Kato problem and extensions for degenerate elliptic operators

David Cruz-Uribe, José María Martell, Cristian Rios

We study the Kato problem for degenerate divergence form operators. This was begun by Cruz-Uribe and Rios who proved that given an operator $L_{w} = - w^{- 1} div (A \nabla)$ , where $…

math.CA2015★ 2 cited

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 $Ω \subset R^{n + 1}$ , $n \geq 1$ , and any $E \subset \partial Ω$ with $0<\mathcal{H}^n(E)<\…

math.CA2015★ 61 cited

Rectifiability of harmonic measure

Jonas Azzam, Steve Hofmann, José María Martell +4

In the present paper we prove that for any open connected set $Ω \subset R^{n + 1}$ , $n \geq 1$ , and any $E \subset \partial Ω$ with $H^{n} (E) < \infty$ , absolute continui…

math.AP2015★ 6 cited

Absolute continuity between the surface measure and harmonic measure implies rectifiability

Steve Hofmann, José Maria Martell, Svitlana Mayboroda +2

In the present paper we prove that for any open connected set $Ω \subset R^{n + 1}$ , $n \geq 1$ , and any $E \subset \partial Ω$ with $0 < H^{n} (E) < \infty$ absolute contin…

math.CA2015★ 26 cited

Oscillation estimates, self-improving results and good- $λ$ inequalities

Lauri Berkovits, Juha Kinnunen, José María Martell

Our main result is an abstract good- $λ$ inequality that allows us to consider three self-improving properties related to oscillation estimates in a very general context. The novelt…

math.CA2015★ 24 cited

Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries

Murat Akman, Matthew Badger, Steve Hofmann +1

Let $Ω \subset R^{n + 1}$ , $n \geq 2$ , be 1-sided NTA domain (aka uniform domain), i.e. a domain which satisfies interior Corkscrew and Harnack Chain conditions, and assume th…

math.CA2015★ 27 cited

Uniform Rectifiability and harmonic measure IV: Ahlfors regularity plus Poisson kernels in $L^{p}$ implies uniform rectifiability

Steve Hofmann, J. M. Martell