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2019 Invertibility of operators on atomic subspaces of $L^1$ and an application to the Neumann problem
Hugo Ocampo-Salgado, Jorge Rivera-Noriega
Rocky Mountain J. Math. 49(3): 929-944 (2019). DOI: 10.1216/RMJ-2019-49-3-929

Abstract

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 $L^1$.

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Hugo Ocampo-Salgado. Jorge Rivera-Noriega. "Invertibility of operators on atomic subspaces of $L^1$ and an application to the Neumann problem." Rocky Mountain J. Math. 49 (3) 929 - 944, 2019. https://doi.org/10.1216/RMJ-2019-49-3-929

Information

Published: 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07088344
MathSciNet: MR3983308
Digital Object Identifier: 10.1216/RMJ-2019-49-3-929

Subjects:
Primary: 31B10, 42B35
Secondary: 31B20, 46E30

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 3 • 2019
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