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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)

Biographic References:

Sobolev, S. L.
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