Published Paper

Inserted: 26 oct 2023
Last Updated: 26 oct 2023

Journal: Mathematical Notes
Volume: 114
Number: 3
Pages: 351--376
Year: 2023
Doi: 10.1134/S0001434623090079

Abstract:

Let $(\operatorname{X},\operatorname{d},\mu)$ be a metric measure space with uniformly locally doubling measure $\mu$. Given $p \in (1,\infty)$, assume that $(\operatorname{X},\operatorname{d},\mu)$ supports a weak local $(1,p)$-Poincar\'{e} inequality. We characterize trace spaces of the first-order Sobolev $W_{p}^{1}(\operatorname{X})$-spaces to subsets $S$ of $\operatorname{X}$ that can be represented as a finite union $\cup_{i=1}^{N}S^{i}$, $N \in \mathbb{N}$, of Ahlfors–David regular subsets $S^{i} \subset \operatorname{X}$, $i \in \{1,...,N\}$, of different codimensions. Furthermore, we explicitly compute the corresponding trace norms up to some universal constants.

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