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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Traces of BMO-Sobolev spaces


Author: Robert S. Strichartz
Journal: Proc. Amer. Math. Soc. 83 (1981), 509-513
MSC: Primary 46E35
DOI: https://doi.org/10.1090/S0002-9939-1981-0627680-8
MathSciNet review: 627680
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Abstract: The trace operator $ RF(x) = F(x,0)$ where $ F(x,t)$ is a function of $ x \in {{\mathbf{R}}^n}$ and $ t \in {{\mathbf{R}}^1}$ maps $ {I_\alpha }(BMO)$, the $ BMO$-Sobolev space of Riesz potentials of order $ \alpha $ of functions of bounded mean oscillation on $ {{\mathbf{R}}^{n + 1}}$, onto the homogeneous Besov space $ \Lambda _\alpha ^0(\infty ,\infty )$ on $ {{\mathbf{R}}^n}$, for $ \alpha > 0$. A right inverse is given by the extension operator $ Ef(x,t) = {\mathcal{F}^{ - 1}}({e^{ - {t^2}{{\left\vert \xi \right\vert}^2}}}\hat f(\xi ))$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627680-8
Keywords: Bounded mean oscillation, Sobolev space, Besov space, trace theorem
Article copyright: © Copyright 1981 American Mathematical Society