On the extension of VMO functions
| Autor: | Butaev, Almaz, Dafni, Galia |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider functions of vanishing mean oscillation on a bounded domain $\Omega$ and prove a $\rm{VMO}$ analogue of the extension theorem of P. Jones for $\rm{BMO}(\Omega)$. We show that if $\Omega$ satisfies the same condition imposed by Jones (i.e.\ is a uniform domain), there is a linear extension map from $\rm{VMO}(\Omega)$ to $\rm{VMO}(\mathbb{R}^n)$ which is bounded in the $\rm{BMO}$ norm. Moreover, if such an extension map exists from $\rm{VMO}(\Omega)$ to $\rm{BMO}(\mathbb{R}^n)$, then the domain is uniform. Comment: 26 pages |
| Databáze: | arXiv |
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