Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications - Wu Ruimin; Wang Songbai (Open Mathematics, 2023)
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,φ }\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 φφ -capacity and studied some of its properties.