The Equivalence Relations between the Ditzian]Totik Moduli of Smoothness and Best Polynomial Approximation in the Besov Spaces

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 p with 1FpF` and a, s 1FsF`. 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