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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.01385 |
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Table of Contents:
- In the setting of a non-complete doubling metric measure space $(Ω,d,μ)$, we construct various bounded linear trace and extension operators for homogeneous and inhomogeneous Besov spaces $B^α_{p,q}$. Equipping the boundary $\partialΩ:=\overlineΩ\setminusΩ$ with a measure which is codimension $θ$ Ahlfors regular with respect to $μ$, these operators take the form \[ T:B^α_{p,q}(Ω)\to B^{α-θ/p}_{p,q}(\partialΩ),\quad E:B^α_{p,q}(\partialΩ)\to B^{α+θ/p}_{p,q}(Ω). \] The trace operators are first constructed under the additional assumption that $Ω$ is a uniform domain in its completion. We then use such results along with the technique of hyperbolic filling to remove this assumption in the case that $Ω$ is bounded. This extends to the doubling setting some earlier results of Marcos and Saksman-Soto proven under the assumption that the ambient measure is Ahlfors regular.