2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157316We 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.11 pagesAnalysis of PDEsFunctional Analysis58A12, 46E30text