## Compact and continuous embeddings of logarithmic Bessel potential spaces.(English)Zbl 1083.46017

The paper deals with continuous and compact embeddings of the refinement $$H^\sigma L_{p,q;\alpha_1, \dots, \alpha_m} (\Omega)$$ of the Bessel potential spaces $$H^\sigma_p (\Omega)$$ into generalised Lorentz–Zygmund spaces $$L_{r,q;\alpha_1, \dots, \alpha_m} (\Omega)$$ and generalised Hölder spaces $$C^{0, \lambda (\cdot)} (\bar{\Omega})$$. Here, $$1<p< \infty$$ and $$\Omega$$ stands for $$\mathbb R^n$$ or a bounded domain in $$\mathbb R^n$$. Furthermore, $$L_{p,q}$$ are the usual Lorentz–Zygmund spaces, while the $$\alpha_1, \dots, \alpha_n$$ refer to logarithmic refinements and $$\lambda$$ indicates a generalised modulus of continuity.

### MSC:

 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Full Text: