Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications

Abstract

Let m∈Nm\in {\mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces Wm,φ(Rn){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.

Keywords

• interpolation inequality
• generalized orlicz-sobolev space
• maximal function operator
• 26d10
• 46e30
• 46e35