TITLE: Are $C^n$ smoothness classes defined for fractional $n$?
QUESTION [1 upvotes]: Are $C^n$ smoothness classes defined for fractional $n$?
What is the definition?

REPLY [1 votes]: Yes it is. I didn't bother to write it out but take a look at Hölder condition
EDIT: As noted in the comments Sobolev spaces are indeed a generalization. And they are nicely connected by the Sobolev embedding theorem
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