Function classes, constructed on the basis of averages. (Dedicated to S. L. Sobolev in connection with his eightieth anniversary). (Russian) Zbl 0665.46027
The authors investigate function classes introduced by means of averaging over a sphere. It is shown that these classes coincide with the well known Nikol’skij spaces \(H^ r_ p\) or Besov spaces \(B^ r_{p,\theta}\).
Reviewer: B.Opic
MSC:
46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
41A30 | Approximation by other special function classes |
41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |