Besov spaces on closed subsets of $\textbf {R}^ n$
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- by Alf Jonsson
- Trans. Amer. Math. Soc. 341 (1994), 355-370
- DOI: https://doi.org/10.1090/S0002-9947-1994-1132434-6
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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 ${L^p}$.References
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Bibliographic Information
- © Copyright 1994 American Mathematical Society
- 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