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

Abstract

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

5 pages

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