Extension Theorems on Weighted Sobolev Spaces and Some Applications We extend the extension theorems to weighted Sobolev spaces $L^p_{w,k}(\mathcal D)$ on $(\varepsilon,\delta)$ domains with doubling weight $w$ that satisfies a Poincar\'e inequality and such that $w^{-1/p}$ is locally $L^{p'}$. We also make use of the main theorem to improve weighted Sobolev interpolation inequalities. Keywords:PoincarÃ© inequalities, $A_p$ weights, doubling weights, $(\ep,\delta)$ domain, $(\ep,\infty)$ domainCategory:46E35