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Let $0<\alpha<n$, $1<p<q<\infty$ and $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{n}$. Then:

$$\left\|\int_{\mathbb{R}^n} \frac{f(y)dy}{|x-y|^{n-\alpha}} \right\|_{L^q(\mathbb{R}^n)} \leq C\left\| f \right\|_{L^p(\mathbb{R}^n)}$$.

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Would you mind and formulate a question? – Dirk Oct 19 '12 at 10:46
thank you norbert! – Felice Oct 19 '12 at 11:44

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