Characterization of anysotropic Liouville-type mixed spaces and its application
Abstract
Description
Within 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 pages
LaTex, 23 pages