We prove a criterion for invertibility of operators on adequate adaptations to the boundary of a smooth domain of atomic subspaces of $L^1$, originally defined on ${\mathbb{R}^n} $ by Sweezy. As an application, we establish solvability of the Neumann problem for harmonic functions on smooth domains, assuming that the normal derivative belongs to said atomic subspaces of $L^1$.
Rocky Mountain J. Math.
49(3):
929-944
(2019).
DOI: 10.1216/RMJ-2019-49-3-929
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