Sobolev type inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund spaces on homogeneous groups

摘要: We define Euler-Hilbert-Sobolev spaces and obtain embedding results on homogeneous groups using Euler operators, which are differential operators of order zero. Sharp remainder terms $L^{p}$ weighted Sobolev type Sobolev-Rellich inequalities given. Most obtained with best constants. As consequences, we analogues the generalised classical inequalities. also discuss applications logarithmic Hardy to Sobolev-Lorentz-Zygmund spaces. The new already in anisotropic $\mathbb R^{n}$ as well isotropic due freedom choice any quasi-norm.