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We study the boundary integral operator induced from the fractional Laplaceequation in a bounded smooth domain. For $1/2 < \alpha? < 1$, we show thebijectivity of the boundary integral operator $S_{2\alpha} : L^p(\partial\Omega) \rightarrow H^{2\alpha-1}_p (\partial \Omega), 1 < p < 1$. As anapplication, we show the existence of the solution of the boundary valueproblem of the fractional Laplace equation.

Boundary integral operator for the fractional Laplacian in the bounded smooth domain