Renormings of $L^p(L^q)$
  We investigate the best order of smoothness of $L^p(L^q)$. We prove in particular that there exists a $C^\infty$-smooth bump function on $L^p(L^q)$ if and only if $p$ and $q$ are both even integers and $p$ is a multiple of $q$. 
R. Deville (Univ. Bordeaux), R. Gonzalo (Univ. Complutense) and J.A.   Jaramillo (Univ. Complutense)