Differentiable mappings on products with different degrees of   differentiability in the two factors
  We develop differential calculus of $C^{r,s}$-mappings on products of locally convex spaces and prove exponential laws for such mappings. As an application, we consider differential equations in Banach spaces depending on a parameter in a locally convex space. Under suitable assumptions, the associated flows are mappings of class $C^{r,s}$. 
Hamza Alzaareer and Alexander Schmeding
math.FA