Nikol’skij, S. M.; Lizorkin, P. I. Function classes, constructed on the basis of averages. (Dedicated to S. L. Sobolev in connection with his eightieth anniversary). (Russian) Zbl 0665.46027 Sib. Mat. Zh. 29, No. 5(171), 181-190 (1988). 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 Cited in 1 Review 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) Keywords:approximation by means of entire functions of exponential type; function classes; averaging over a sphere; Nikol’skij spaces; Besov spaces Biographic References: Sobolev, S. L. PDFBibTeX XMLCite \textit{S. M. Nikol'skij} and \textit{P. I. Lizorkin}, Sib. Mat. Zh. 29, No. 5(171), 181--190 (1988; Zbl 0665.46027) Full Text: EuDML