Given $0 < \alpha < 1$, consider the Holder space $C^{0,\alpha}(\overline{U})$. Is there any nice subspace of all of these Holder spaces? In other words, whats is $$ \bigcap_{0 < \alpha < 1} C^{0,\alpha}(\overline{U}) ? $$ Under some conditions this intersection could be not empty?
2026-03-29 14:57:37.1774796257
Intersection of all Holder spaces
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