O. Tapiola

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20182020

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math.AP2020

Uniform rectifiability implies Varopoulos extensions

Steve Hofmann, Olli Tapiola

We construct extensions of Varopolous type for functions $f \in BMO (E)$ , for any uniformly rectifiable set $E$ of codimension one. More precisely, let $Ω\subset \mathbb{R}^{…

math.AP2018

$ε$ -Approximability of Harmonic Functions in $L^{p}$ Implies Uniform Rectifiability

Simon Bortz, Olli Tapiola

Suppose that $Ω \subset R^{n + 1}$ , $n \geq 2$ , is an open set satisfying the corkscrew condition with an $n$ -dimensional ADR boundary, $\partial Ω$ . In this note, we show tha…

Uniform rectifiability implies Varopoulos extensions

ε-Approximability of Harmonic Functions in Lp Implies Uniform Rectifiability

$ε$ -Approximability of Harmonic Functions in $L^{p}$ Implies Uniform Rectifiability