Abstract. The authors estimate the best algebraic approximation error of the locally absolutely continuous functions in the space $L_u^p([-1,1])$, where $u$ is a generalized Ditzian--Totik weight. A simultaneous approximation theorem is shown for the Fourier projector corresponding to the generalized Jacobi polynomials. Finally, the boundedness of the Lagrange interpolation operator is proved in a space of Sobolev-type.

AMS Subject Classification (1991): 41A05

Received September 28, 1994 and in revised form December 8, 1994. (Registered under 5623/2009.)