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Better Sobolev inequality holds in this case when assuming doubling and Poincare inequality?
Let $X$ be a Polish space and let $m$ be a locally finite Borel measure on $X$.
Let $\epsilon$ be a strongly local, regular Dirichlet form on $L^2(X,m)$ with Domain $V :=\{f\in L^2(X,m):\epsilon(f)&...
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