Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications

作者：Wu, Ruimin^*; Wang, Songbai

来源：Open Mathematics, 2023, 21(1): 20220595.

DOI：10.1515/math-2022-0595

• interpolation inequality
• generalized Orlicz-Sobolev space
• maximal function operator

Let m ? N and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces W-m,W-f(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 f-capacity and studied some of its properties.