Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications

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