Traces of Sobolev spaces to irregular subsets of metric measure spaces

2022/12/21 by Alexander Tyulenev, Tyulenev, Alexander
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.11271

openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given p ∈ (1,∞), let (X,d,μ) be a metric measure space with uniformly locally doubling measure μ supporting a weak local (1,p)-Poincaré inequality. For each θ∈ [0,p), we characterize the trace space of the Sobolev W¹_p(X)-space to lower codimension-θ content regular closed subsets S ⊂ X. In particular, if the space (X,d,μ) is Ahlfors Q-regular for some Q ≥ 1 and p ∈ (Q,∞), then we get an intrinsic description of the trace-space of the Sobolev W¹_p(X)-space to arbitrary closed nonempty set S ⊂ X.

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