Borderline case of traces and extensions for weighted Sobolev spaces
Functional Analysis
2021-09-29 v1
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.
Cite
@article{arxiv.2109.13505,
title = {Borderline case of traces and extensions for weighted Sobolev spaces},
author = {Manzi Huang and Xiantao Wang and Zhuang Wang and Zhihao Xu},
journal= {arXiv preprint arXiv:2109.13505},
year = {2021}
}
Comments
22 pages, 1 figure