Let $ (H, \ | \ |) $ and $ (V, \ | \ | _V) $ be two separable Hilbert spaces with $ V $ is injected densely and continuously into $ H $ which is identified with its dual $ H '$ consequently $$ V \underset{d}{\hookrightarrow} H \approxeq H '\underset{d}{\hookrightarrow}V' $$ With $ V'$ \ is \ the \ dual \ of \ $V$.
My question is : there is a relation (of embedding for example) between the interpolation space $ [V '; V] _ {1/2; 2} $ and $ H $ in particular ?, and generally between $ [V '; V] _ {1-1 / p; p} $ and $ H $ for $ p> 1 $? Thank you very much.