We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonlocal Dirichlet problem. We give a Douglas-type formula for the quadratic form of the Poisson extension. 2 R d ×R d \D c ×D c (u(x) − u(y)) 2 ν(x, y) dxdy.
Abstract. We prove the existence of the integrated density of states for subordinate Brownian motions in presence of the Poissonian random potentials on the Sierpiński gasket.
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