On the Nikol’skii and Potapov classes of functions
Tóm tắt
It is proved that the Nikol’skii classes H
1
r
and Potapov classes A
1
r
contain the class W
1
r
for r > 1/2.
Tài liệu tham khảo
M. K. Potapov, “On Jackson type theorems in the L p metric,” Dokl. Akad. Nauk SSSR 111 (6), 1185–1188 (1956).
M. K. Potapov, “On the approximation of nonperiodic functions by algebraic polynomials,” Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., No. 4, 14–25 (1960).
M. K. Potapov, “On approximation by algebraic polynomials in the L p metric,” in Studies on Modern Problems of Constructive Function Theory (Fizmatgiz, Moscow, 1961), pp. 64–69 [in Russian].
V. P. Motornyi, “Approximation of functions by algebraic polynomials in the L p metric,” Izv. Akad. Nauk SSSR, Ser. Mat. 35 (4), 874–899 (1971) [Math. USSR, Izv. 5, 889–914 (1971)].