I would need some help in prove some properties of Holder Spaces. I should prove that $C^{1,\alpha}(X) \subseteq \subseteq C^{0,\beta}(X)$ for $\alpha,\beta\in (0,1), X=[a,b]$. I can prove the fact that $C^{1,\alpha} \subseteq \subseteq C^1$ but there is left to prove that $C^1 \subseteq C^{0,\beta}$. So that differentiable funtions are Holder continuous. Any ideas?
2026-03-25 14:00:34.1774447234
Complete Imbreeding.Holder Spaces. Functional Analysis
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