In the book "Interpolation theory, function spaces, differential operators" by Hans Triebel, I tried to understand the result Theorem~1(a) of section~2.4.2. In particular, I am interested in the following result:
Suppose, $1<p_0<p<p_1<\infty$ be such that, for some $\theta\in(0,1)$, $\frac{1}{p}=\frac{1-\theta}{p_0}+\frac{\theta}{p_1}$ and $s=(1-\theta)s_0+\theta s_1$. Then we have $B^s_{p,p}=\left( H^{s_0}_{p_0},H^{s_1}_{p_1}\right)_{\theta,p}$.
Frankly speaking, I did not understand it. Its proof is not given directly; rather, we are supposed to trace back an array of theorems to understand it. Being an absolute beginner in these topics (interpolation and Besov spaces, etc.), I decided to look for the result in other places, but without luck.
Can you suggest some references where I can get what I am looking for? I know the modern approach for fractional Sobolev spaces, as given here.
PS: 1) I read only the K-method of real interpolation from Triebel's book, mentioned above. 2) For me, these spaces mentioned in the theorem are defined via difference quotients and Bessel potentials respectively.