Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications

Abstract

Abstract Let m ∈ N m\in {\mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces W m , φ ( R n ) {W}^{m,\varphi }\left({{\mathbb{R}}}^{n}) . As applications, we established a compact Sobolev embedding on domain and a Landau-Kolmogorov-type inequality in generalized Orlicz spaces. And we introduced the Sobolev φ \varphi -capacity and studied some of its properties.