I've recently read about the notion of (Rademacher) type and cotype of a Banach space in some article. In the books I checked afterwards, typical examples studied were $L^p$-spaces or the Schatten classes but nothing was said about spaces of continuous functions. As these are arguably one of the most important examples of Banach spaces, I wonder why this is. 


So here is my question: Is anything known about the type and/or cotype of the Banach space $C(K)$ with suitable $K$? 


I'm particularly interested in the case where $K$ is a compact interval on the real line.



type and cotype of spaces of continuous functions
It is known that $C(K)$, for infinite $K$, contains a copy of $c\_0$, hence it does not have nontrivial type (meaning $>1$) or nontrivial cotype (meaning $<\infty$).


