Asymptotics properties of a compact set of smooth functions in the space of functions of bounded \(p\)-variation (Q1907402)

The author improves the estimates of the \(\varepsilon\)-entropy and of the Kolmogorov widths of the compact sets of functions with a given majorant of the continuity modulus of order \(k= {1\over p}\) of the \(r\)-th derivative. In special cases these estimates have been earlier obtained by the same author in [Vestn. Mosk. Univ., Ser. I 1992, No. 5, 81-84 (1992; Zbl 0802.46048)] for \(r>0\) and in [Izv. Vysh. Uchebn. Zaved., Mat. 1992, No. 2(357), 83-85 (1992; Zbl 0820.41020)] for \(r=0\) and \(k=1\).