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

We study the boundary integral operator induced from the fractional Laplace equation in a bounded smooth domain. For $1/2 < α? < 1$, we show the bijectivity of the boundary integral operator $S_{2α} : L^p(\partial Ω) \rightarrow H^{2α-1}_p (\partial Ω), 1 < p < 1$. As an application, we show the existence of the solution of the boundary value problem of the fractional Laplace equation.

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