Open Access
2001/2002 Sobolev Extension Domains on Metric Spaces of Homogeneous Type
Petteri Harjulehto
Real Anal. Exchange 27(2): 583-598 (2001/2002).


Let $(X,d,\mu)$ be a metric measure space of homogeneous type with a finite measure. Assume that $\Omega \subset X$ is a bounded domain, which satisfies an $A^*(\varepsilon,\delta)$-condition and $\mu(\partial\Omega)=0$. We show that there exists a bounded linear extension operator $Ext$ from the Hajłasz space $M^{1,p}(\Omega,d,\mu)$ to $M^{1,p}(X,d,\mu)$, such that $Ext (u)\vert_\Omega = u$.


Download Citation

Petteri Harjulehto. "Sobolev Extension Domains on Metric Spaces of Homogeneous Type." Real Anal. Exchange 27 (2) 583 - 598, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 2 June 2008

zbMATH: 1082.46024
MathSciNet: MR1922670

Primary: 46E35

Keywords: extension domain , Haj\l asz space , metric space of homogeneous type , Sobolev space

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 2 • 2001/2002
Back to Top