Polynomial Approximation on C^2 -Domains

We introduce appropriate computable moduli of smoothness to characterize the rate of best approximation by multivariate polynomials on a connected and compact C^2 -domain Ω⊂ℝ^d . This new modulus of smoothness is defined via finite differences along the directions of coordinate axes, and along a number of tangential directions from the boundary. With this modulus, we prove both the direct Jackson inequality and the corresponding inverse for the best polynomial approximation in L_p(Ω ) . The Jackson inequality is established for the full range of 0更多