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Sobolev extension via reflections

· 2018 · math.FA · arXiv 1812.09037

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abstract

We show that the extension results by Mazya and Poborchi for polynomial planar cusps can be realized via composition operators generated by reflections.

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math.FA 1

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2019 1

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CONDITIONAL 1

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Extension operators on Sobolev spaces with decreasing integrability

math.FA · 2019-08-25 · conditional · novelty 5.0

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 math.FA · 2019-08-25 · conditional · none · ref 14 · internal anchor

    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.