  We extend some results by Gol'dshtein, Kuz'minov, and Shvedov about the
$L_p$-cohomology of warped cylinders to $L_{p,q}$-cohomology for different $p$
and $q$. As an application, we establish some sufficient conditions for the
nontriviality of the $L_{p,q}$-torsion of a surface of revolution in terms of
some Hardy constants.
