TITLE: Symbol for twice differentiable functions
QUESTION [5 upvotes]: Is there a symbol for the set of twice differentiable functions (2nd derivative not necessarily continuous)? I believe the symbol for twice continuously differentiable functions is $C^2(\mathbb F)$? Thanks

REPLY [5 votes]: Given your tag of functional analysis, the following might be of interest for you:
The Sobolev space $W^{k,p}(\Omega)$ is the set of all functions $f \in L^p(\Omega)$ such that for every  multi-index $\alpha$ $|α| \leq k$, the weak partial derivative $D^\alpha f$ belongs to $L^p(\Omega)$.
More details in Wikipedia.