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

摘要

An inverse theorem for the best weighted polynomial approximation of a function in L~q_wα(S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L_p(R)_wλ, where ωα 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.