We obtain matching direct and inverse theorems for the degree of weighted Lp-approximation by polynomials with the Jacobi weights (1−x)α(1+x)β. Combined, the estimates yield a constructive characterization of various smoothness classes of functions via the degree of their approximation by algebraic polynomials. In addition, we prove Whitney type inequalities which are of independent interest.
- Approximation by polynomials in weighted L-norms
- Characterization of smoothness classes
- Degree of approximation
- Direct and inverse theorems
- Jacobi weights
- Moduli of smoothness
- Whitney-type estimates