J. Garnett

activity

20092022

most citedUniform rectifiability from Carleson measure estimates and

ε

-approximability of bounded harmonic functions

29 citations · 53 across the 8 of their papers we have counts for

collaborators

Showing math.CAShow all

5 papers · 1 filter

math.CA2022

On Extrapolation of Carleson Measures

John Garnett

We give an alternate proof of three versions of the theorem on extrapolation of Carleson measures.

math.CA2020

Carleson measure estimates and $ε$ -approximation of bounded harmonic functions, without Ahlfors regularity assumptions

John Garnett

Let $Ω$ be a domain in $R^{d + 1}$ , $d \geq 1$ . In the paper's references [HMM2] and [GMT] it was proved that if $Ω$ satisfies a corkscrew condition and if $\partial Ω$ is $…

math.CA2016★ 29 cited

Uniform rectifiability from Carleson measure estimates and $ε$ -approximability of bounded harmonic functions

John Garnett, Mihalis Mourgoglou, Xavier Tolsa

Let $Ω \subset R^{n + 1}$ , $n \geq 1$ , be a corkscrew domain with Ahlfors-David regular boundary. In this paper we prove that $\partial Ω$ is uniformly $n$ -rectifiable if every bo…

math.CA2016★ 18 cited

Uniform rectifiability, elliptic measure, square functions, and $ε$ -approximability via an ACF monotonicity formula

Jonas Azzam, John Garnett, Mihalis Mourgoglou +1

Let $Ω \subset R^{n + 1}$ , $n \geq 2$ , be an open set with Ahlfors-David regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator $L$ i…

math.CA2014★ 2 cited

Square functions and uniform rectifiability

Vasilis Chousionis, John Garnett, Triet Le +1

In this paper it is shown that an Ahlfors-David $n$ -dimensional measure $μ$ on $R^{d}$ is uniformly $n$ -rectifiable if and only if for any ball $B (x_{0}, R)$ centered at $\oper…

On Extrapolation of Carleson Measures

Carleson measure estimates and ε-approximation of bounded harmonic functions, without Ahlfors regularity assumptions

Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions

Uniform rectifiability, elliptic measure, square functions, and ε-approximability via an ACF monotonicity formula

Square functions and uniform rectifiability

Carleson measure estimates and $ε$ -approximation of bounded harmonic functions, without Ahlfors regularity assumptions

Uniform rectifiability from Carleson measure estimates and $ε$ -approximability of bounded harmonic functions

Uniform rectifiability, elliptic measure, square functions, and $ε$ -approximability via an ACF monotonicity formula