Those differential operators that are bounded.

Question

Differential operators are known as unbounded operators, but there always are some exceptions. Does anyone know an example of a differential operator on appropriate Sobolev spaces that is not unbounded?

thanks for helping me.

Answer 1

For Example: $A:H_0^1(I) \to L^2(I)$

$Af=df/dx$

but be careful $A:L^2(I) \to L^2(I)$, with the same definition, is not bounded.