K-Functional, Weighted Moduli of Smoothness, and Best Weighted Polynomial Approximation on a Simplex  

作　　者：Song Li Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China 

出　　处：《Acta Mathematica Sinica,English Series》1999年第3期395-403,405-406,共11页数学学报（英文版）

摘　　要：An inverse theorem for the best weighted polynomial approximation of a function in L_{w_α}^p（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L_p（R）w_λ, where w_α is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W_λ is a Freud weight. For Ditzian-Totik K-functionals on L_P（S）, 1≤P≤∞, we obtain a new equivalence expression.An inverse theorem for the best weighted polynomial approximation of a function in L_{w_α}^p（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L_p（R）w_λ, where w_α is a Jacobi-type weight on S, 0<p≤∞, S is a simplex and W_λ is a Freud weight. For Ditzian-Totik K-functionals on L_P（S）, 1≤P≤∞, we obtain a new equivalence expression.

关 键 词：Weighted moduli of smoothness K-FUNCTIONAL Best weighted polynomial approximation SIMPLEX 

分 类 号：O1[理学—数学]