Sobolev embedding implies regularity of measure in metric measure spaces
| Autor: | Karak, Nijjwal |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove that if the Sobolev embedding $M^{1,p}(X)\hookrightarrow L^q(X)$ holds for some $q>p\geq 1$ in a metric measure space $(X,d,\mu),$ then a constant $C$ exists such that $\mu(B(x,r))\geq Cr^n$ for all $x\in X$ and all $0 |
| Databáze: | arXiv |
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