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

Abstract

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 $q$.Comment: 18 pages; AMS-Te