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1. CJM 2006 (vol 58 pp. 492)
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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:Poincaré inequalities, $A_p$ weights, doubling weights, $(\ep,\delta)$ domain, $(\ep,\infty)$ domain Category:46E35 |