What happen with $p=\infty$ interpolation spaces

Question

Hy all

I am reading the following book, theorem 5.4.1 page 115.

Interpolation Spaces: An Introduction Volume: Author(s): Jöran Bergh, Jörgen Löfström (auth.) link http://libgen.rs/book/index.php?md5=11896EB4497FAEA24470EC91FBBED428

The theorem say: Assume that $0<p\leq \infty$ and $\theta\in (0,1)$. Put $w(x)=w_0^{1-\theta}(x)w_1^{\theta}(x)$ then $(L_p(w_0,L_p(w_1))_{\theta,p}=L_p(w)$.

I understander the proof. My problem is what happen with $p=\infty$. They defined

$K_p(t,f)=\inf_{f=f_0+f_1}\left(||f_0||_{L_p(w_0)}^p + t^p||f_1||_{L_p(w_1)}^p \right)^{\frac{1}{p}}$ for $0<p\leq \infty$ but how can interpreted the expresion with $p=\infty$

Please, can somebody tell me how interpretate that?

Best