Abstract. The authors estimate the error of best polynomial approximation in $L^p$-weighted spaces with weights having zeros inside $[-1,1],$ using a suitable modulus of smoothness. The Jackson and Stechkin inequalities are given. Moreover some estimates of the derivatives of the polynomials of best approximation are proved.

AMS Subject Classification (1991): 41A10, 41A17, 41A27

Keyword(s): Polynomial Approximation, doubling weight, modulus of smoothness, K-functional

Received October 1, 2001, and in revised form July 22, 2002. (Registered under 2891/2009.)