Renormings of $L^p(L^q)$

R. Deville, R. Gonzalo, J. A. Jaramillo

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 b…