Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications

Let and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces . 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 -capacity and studied some of its properties.