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What is the widely used notation to denote the class of Lipschitz continuous functions?

i.e. suppose $f$ is continuously differentiable, then $f \in C^1$

Fraïssé
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1 Answers1

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Lipschitz functions are a special case of Holder continuous functions. The class of functions that are Holder continuous with coefficient $\alpha$ is a Banach space and is commonly denoted $C^{k,\alpha}$. Lipschitz functions are the special case with $\alpha = 1$, so you will often see them denoted $C^{k,1}$. I do not recall seeing some other specific notation for Lipschitz functions in the literature.

Update: Over more recent months I did run across the notation $\text{Lip}(X)$ for the space of Lipschitz functions on a measure space $X$.

Gyu Eun Lee
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  • You forgot to mention that Lipshitz functuons are the special case with $\alpha=1$ AND $ k=0$. Also, do you mean a metric space at the end? Other than those minor issues I agree with both your proposals – Bananach Jul 13 '16 at 10:36