Lipschitz spaces over non-porous sets

2025/07/16 by Aliaga, Ramón J. · 1 citation
#46B03 #46E15 #53C17 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.12119

Abstract

Let M be a subset of ℝⁿ. If M is not porous, in particular if it has positive n-dimensional Lebesgue measure, we prove that the Lipschitz spaces Lip₀(M) and Lip₀(ℝⁿ) are linearly isomorphic. The result also holds more generally if ℝⁿ is replaced with a Carnot group equipped with its Carnot-Carathéodory metric.

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