Multivariate Weighted Modulus of Smoothness and Bernstein-Durrmeyer Operators in B_a Space
Ba空间中的多元加权光滑模与Bernstein Durrmeyer算子

In this paper, the authors introduce a new multivariate weighted modulus of smoothness in B-a space, which generalizes the Ditzian-Totik's modulus in L p space. The equivalence relationship between the modulus and certain K-functional is shown. As an application, the relationship between the multivariate Bernstein-Durrmeyer operators defined on the simplex and the modulus is discussed as well. Namely, with the modulus as a metric, the upper and lower bounds of degree of approximation by the operators are estimated in B-a space.