Let $X$ denote an open subset of $\mathbb{R}^n$. Suppose $n \in \{0, 1, \dots\}$, $0 < \gamma \le 1$. Does it necessarily follow that $C^{n, \gamma}(\overline{X})$ is a Banach space?
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https://en.wikipedia.org/wiki/Sobolev_space please explain your notation and see https://en.wikipedia.org/wiki/Lp_space#When 0 < p < 1 – reuns Feb 21 '16 at 23:30
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I didn't know those, and it is said that it is a Banach space https://en.wikipedia.org/wiki/H%C3%B6lder_condition#H.C3.B6lder_spaces if $X$ is bounded – reuns Feb 21 '16 at 23:47