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Transactions of the American Mathematical Society

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Besov spaces on closed subsets of $ {\bf R}\sp n$


Author: Alf Jonsson
Journal: Trans. Amer. Math. Soc. 341 (1994), 355-370
MSC: Primary 46E35
DOI: https://doi.org/10.1090/S0002-9947-1994-1132434-6
MathSciNet review: 1132434
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Abstract: Motivated by the need in boundary value problems for partial differential equations, classical trace theorems characterize the trace to a subset $ F$ of $ {\mathbb{R}^n}$ of Sobolev spaces and Besov spaces consisting of functions defined on $ {\mathbb{R}^n}$, if $ F$ is a linear subvariety $ {\mathbb{R}^d}$ of $ {\mathbb{R}^n}$ or a $ d$-dimensional smooth submanifold of $ {\mathbb{R}^n}$. This was generalized in [2] to the case when $ F$ is a $ d$-dimensional fractal set of a certain type. In this paper, traces are described when $ F$ is an arbitrary closed set. The result may also be looked upon as a Whitney extension theorem in $ {L^p}$.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1132434-6
Article copyright: © Copyright 1994 American Mathematical Society

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