On interpolation and on traces of functions of some anisotropic functional spaces. (Russian. English summary) Zbl 0674.46045
An anisotropic analogue of the space of Bessel potentials is considered. It is proved that while interpolating such spaces by means of the real interpolation method (anisotropy and summability are fixed, only smoothness varies) one obtains a corresponding anisotropic Besov space. As a consequence a description of the traces for some weighted classes of the spaces of Bessel potentials is obtained.
Reviewer: A.Bukhvalov
MSC:
| 46M35 | Abstract interpolation of topological vector spaces |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
