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arXiv · 2109.13505

Borderline case of traces and extensions for weighted Sobolev spaces

Manzi Huang·Xiantao Wang·Zhuang Wang·Zhihao Xu
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Abstract

In this paper, we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases. We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces, and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces (on hyperplanes) which are defined by using integral averages over selected layers of dyadic cubes.

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Manzi Huang, Xiantao Wang, Zhuang Wang, Zhihao Xu. 2021-09-28. Borderline case of traces and extensions for weighted Sobolev spaces. https://arxiv.org/abs/2109.13505

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