Notation for the sets of locally Lipschitz continuous and differentiable functions

Question

Are there any standard notation for denoting the following sets?

• the set of locally Lipschitz continuous functions, $f\colon \mathbb{R}^n\to \mathbb{R}^m$;
• the set of differentiable functions, $f\colon \mathbb{R}^n\to \mathbb{R}^m$.