Sobolev embedding implies regularity of measure in metric measure spaces

2019/03/06 by Karak, Nijjwal
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1903.02342

Abstract

We prove that if the Sobolev embedding M^1,p(X)\hookrightarrow L^q(X) holds for some q>p≥ 1 in a metric measure space (X,d,μ), then a constant C exists such that μ(B(x,r))≥ Crⁿ for all x∈ X and all 0

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