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تسجيل مستخدم جديدFrom Sobolev Inequality to Doubling
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In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.
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The classical sharp Hardy-Littlewood-Sobolev inequality states that, for $1<p, t<infty$ and $0<lambda=n-alpha <n$ with $ 1/p +1 /t+ lambda /n=2$, there is a best constant $N(n,lambda,p)>0$, such that $$ |int_{mathbb{R}^n} int_{mathbb{R}^n} f(x)|x-y|^
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