Traces of functions of $L^1_2$ Dirichlet spaces on the Carathéodory boundary
Volume 235 / 2016
Studia Mathematica 235 (2016), 209-224
MSC: Primary 46E35; Secondary 30C65.
DOI: 10.4064/sm8485-8-2016
Published online: 4 November 2016
Abstract
We prove that any weakly differentiable function with a square integrable gradient can be extended to the Carathéodory boundary of any simply connected planar domain $\varOmega \not =\mathbb R^2$ up to a set of conformal capacity zero. This result is based on the notion of capacitary boundary associated with the Dirichlet space $L^1_2(\varOmega )$.
