On the intermediate spaces and quasi-linearizability of a pair of spaces of Sobolev-Liouville type
The author considers spaces of Sobolev-Liouville type on \({\mathbb R}^n\) with a norm \[ \| f\| =\| F^{-1}(\nu Ff)\| _{L_p({\mathbb R}^n)} \] denoted by \(H_p(\nu)\). Here \(F\) is the Fourier transform, \(1<p<\infty\), and \(\nu\) is a smooth positive weight function satisfying \(| \xi^\gamma D^\gamma \nu(\xi)| \leq c \nu(\xi)\) for \(| \gamma| \leq 1\) and for some constant \(c>0\). It is proved that the couple \(\{H_p(\nu_0),H_p(\nu_1)\}\) is quasilinearizable. As a consequence a trace type theorem for the spaces \(H_p(\nu)\) is derived.
scientific article; zbMATH DE number 1244246