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In this paper we describe an interpolation result for the Sobolev spaces //¿(fi) where Í2 is a bounded domain with a Lipschitz boundary. This result is applied to derive discrete norm estimates related to multilevel preconditioners and multigrid methods in the finite element method. The estimates are valid for operators of order 2m with Dirichlet boundary conditions.doi:10.1090/s0025-5718-1995-1308447-2 fatcat:is66jhcedbfjbamtnrevz5imzy