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Borderline Case of Traces and Extensions for Weighted Sobolev Spaces

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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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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, P. R. China

    Man Zi Huang, Xian Tao Wang, Zhuang Wang & Zhi Hao Xu

Authors
  1. Man Zi Huang
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  2. Xian Tao Wang
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  3. Zhuang Wang
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  4. Zhi Hao Xu
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Corresponding author

Correspondence to Zhuang Wang.

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The authors declare no conflict of interest.

Additional information

The first author was partly supported by NNSF of China (Grant No. 11822105); the second author was partly supported by NNSF of China (Grant Nos. 12071121 and 11720101003); the third author was supported by NNSF of China (Grant No. 12101226)

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Huang, M.Z., Wang, X.T., Wang, Z. et al. Borderline Case of Traces and Extensions for Weighted Sobolev Spaces. Acta. Math. Sin.-English Ser. 39, 1817–1833 (2023). https://doi.org/10.1007/s10114-023-1309-5

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  • DOI: https://doi.org/10.1007/s10114-023-1309-5

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