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Jun 3 at 7:36 comment added Martin Hairer Define $\mathcal{C}^\alpha$ as the closure of $\mathcal{C}^\infty$ under the norm you describe.
Jun 2 at 23:55 comment added mathex @MartinHairer, is there an alternative way to prove continuity at $0$? What must be done in this case to ensure having continuity? This is crucially needed to prove Schauder estimates for Holder-Besov spaces
Jun 2 at 21:33 comment added Martin Hairer $P_rg$ is smooth, but smooth functions aren't dense in $\mathcal{C}^\alpha$, so it cannot hold in general.
Jun 2 at 21:07 history edited Daniele Tampieri CC BY-SA 4.0
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Jun 2 at 19:24 history edited mathex CC BY-SA 4.0
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Jun 2 at 19:18 history edited mathex CC BY-SA 4.0
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Jun 2 at 19:12 history asked mathex CC BY-SA 4.0