interpolation on sobolev spaces

for 0<theta<1
 and a,b be positive numbers then
c=theta*a+(1-theta)*b

then a new sobolev space  S^c is given by  =[S^a ,S^b] for given theta such that  c=theta*a+(1-theta)*b

Reference: Thm 2.6.3 page 92 in Kesavan's book of "functional analysis and applications"
 
Note: Deducing norms is trivial