2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63951Within the framework of the method of hypersingular integrals we obtain a characterization of the anysotropic spaces $L_{\bar p, \bar r}^{\bar α}$. These spaces are defined to consist of functions $f(x)\in L_{\bar r}$ for which $ F^{-1}(\sum_{j=1}^n |ξ_j|^{α_j})Ff\in L_{\bar p}, α_j>0. $ The mentioned characterization is applied to prove the denseness of the class $C_0^\infty$ in $L_{\bar p, \bar r}^{\bar α}$.LaTex, 23 pagesClassical Analysis and ODEstext