Nikol’skii–Besov spaces with a dominant mixed derivative and with a mixed metric: interpolation properties, embedding theorems, trace and extension theorems

In this work, we define Nikol’skii–Besov spaces with a dominant mixed derivative and with a mixed metric. The interpolation properties of these spaces with respect to the anisotropic interpolation method are studied, sharp embedding theorems of different metrics are proved, and sharp trace and extension theorems are proved.