A new space of potentials with densities from the Stepanov class. (English. Russian original) Zbl 0879.46016
Dokl. Math. 51, No. 2, 218-220 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 341, No. 3, 310-312 (1995).
Summary: Here, I introduce a new function space of functions with fractional smoothness of several variables having the integral representation in the form of convolution with the Bessel-MacDonald matrix kernel and the densities from Stepanov class, in which the known Liouville-Sobolev space (space of Bessel potentials) is embedded.
MSC:
| 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.) |
