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Suppose that Ω is the open region in R n above a Lipschitz graph and let d denote the exterior derivative on R n . We construct a convolution operator T which preserves support in Ω, is smoothing of order 1 on the homogeneous function spaces, and is a potential map in the sense that dT is the identity on spaces of exact forms with support in Ω. Thus if f is exact and supported in Ω, then there is a potential u, given by u = T f , of optimal regularity and supported in Ω, such that du = f . Thisdoi:10.5565/publmat_57213_02 fatcat:fobvmhppb5hfxowxn7hc4ipymi