The equivalence relations between the Ditzian-Totik moduli of smoothness and best polynomial approximation in the Besov spaces

[摘要] The best polynomial approximation is closely related to the Ditzian-Totik modulus of smoothness. In 1988, Z. Ditzian and V. Totik gave some equivalences between them and the class of Besov-type spaces B-alpha,s(p) with 1 less than or equal to p less than or equal to infinity and 1 less than or equal to s less than or equal to infinity. We extend these equivalences to the similar Besov-type spaces with 0 < s < 1. We also give some new equivalences by means of the behavior of best polynomial approximation. (C) 1997 Academic Press.

[发布日期] 1997-11-01