On weighted approximation with Jacobi weights

Abstract

We obtain matching direct and inverse theorems for the degree of weighted $L_p$-approximation by polynomials with the Jacobi weights $(1-x{)}^{\alpha }(1+x{)}^{\beta }$. Combined, the estimates yield a constructive characterization of various smoothness classes of functions via the degree of their approximation by algebraic polynomials.

18 pages