If a bounded extension operator from L^1_p(Ω) to L^1_q(R^n) exists with n < q ≤ p, then Ω must satisfy a generalized (p,q)-measure density inequality and a weak equivalence between its intrinsic and Euclidean metrics.
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Extension operators on Sobolev spaces with decreasing integrability
If a bounded extension operator from L^1_p(Ω) to L^1_q(R^n) exists with n < q ≤ p, then Ω must satisfy a generalized (p,q)-measure density inequality and a weak equivalence between its intrinsic and Euclidean metrics.