Sharp pointwise estimates for functions in the Sobolev spaces Hs(Rn)

We obtain the optimal value of the constant K(n,s) in the Sobolev-Nirenberg-Gagliardo inequality $\|\,u\,\|_{L^{\infty}(\mathbb{R}^{n})} \leq K(n,s) \,\|\, u \,\|_{L^{2}(\mathbb{R}^{n})}^{1 - n/(2s)} \|\, u \,\|_{\dot{H}^{s}(\mathbb{R}^{n})}^{n/(2s)}$ where $s > n/2$.

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