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Sobolev extension via reflections

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arxiv 1812.09037 v2 pith:Z3G477YG submitted 2018-12-21 math.FA

Pekka Koskela , ZhengZhu This is my paper · ORCID
classification math.FA
keywords extensionreflectionscompositioncuspsgeneratedmazyaoperatorsplanar
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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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  1. Extension operators on Sobolev spaces with decreasing integrability

    math.FA 2019-08 conditional novelty 5.0 of 10

    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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