Diameters of certain sets in function spaces

The precise values of the diameters (according to A. N. Kolmogorov) of the class H_C in the space C[a, b] and lower bounds for the diameters of the class H_p in the spaceL_p(0, 2) (1p), for any modulus of continuity(), are obtained. The latter bounds give the exact values of the odd-numbered diameters of the class and the exact order of decay of the diameters of the class H₁.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 637–646, May, 1973.In conclusion, the author wishes to thank A. L. Garkavi, A. V. Efimov, and S. B. stechkin for their help.