Abstract
The boundary of a regular tree can be viewed as a Cantor-type set. We equip our tree with a weighted distance and a weighted measure via the Euclidean arc-length and consider the associated first-order Sobolev spaces. We give characterizations for the existence of traces and for the density of compactly supported functions.
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Acknowledgment
The authors would like to thank the referees for their useful comments that especially allowed as to improve on the original versions of Proposition 2.2 and Lemma 3.11.
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All authors have been supported by the Academy of Finland via Centre of Excellence in Analysis and Dynamics Research (project No. 307333). This work was also partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.
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Koskela, P., Nguyen, K.N. & Wang, Z. Trace and Density Results on Regular Trees. Potential Anal 57, 101–128 (2022). https://doi.org/10.1007/s11118-021-09907-2
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DOI: https://doi.org/10.1007/s11118-021-09907-2