Definition of homogeneous Sobolev spaces $\dot W^{-s,q}$

Question

For the homogeneous Sobolev spaces $\dot H^{-s}$, we can define its norm like this: $$\Vert f \Vert_{\dot H^{-s}}=\Vert \Lambda^{-s} f\Vert_{L^2}$$, i.e., we use fractional derivatives to define it. Then can we define $$\Vert f \Vert_{\dot W^{-s,q}}=\Vert \Lambda^{-s} f\Vert_{L^q}$$ for $q \in (1,\infty)$? We can consider the domain as $\mathbb R^2$.