There are two apparently equivalent definition of sub elliptic estimates. A non-positive self-adjoint operator $L$ satisfies a sub-elliptic estimate with $\varepsilon>0$ if either
1) $\exists C>0 s.t.\forall f$ smooth with compact support $\Vert u\Vert_{2\varepsilon}\leq C(\Vert u\Vert+\Vert Lu\Vert)$ or
2)$\exists C>0$ s.t.$\forall f$ smooth with compact support $\Vert u \Vert^{2}_{\epsilon}\leq C'(\Vert u\Vert^2+\langle Lu,u\rangle )$
I cannot see how both 1) and 2) are equivalent - not even how at least one implies the other. Is there an easy way to see this?