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Our main result is that for the given data $F \\in \\dot H^s(\\Om^c), 0 < s<1$, we find the function which satisfies that $\\De^s u =0$ in $\\Om$,\n  $u|_{\\Om^c} =F$ and $|u|_{\\dot{H}^s(\\R)} \\leq c |F|_{\\dot H^s(\\Om^c)}$. 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