Abstract. For this concept moduli of smoothness for weighted $L^p$ spaces on $[-1,1]$ are based on algebraic additions on $[-1,1]$ where the additions depend on the weight functions. We first investigate algebraic and differential properties of the additions which will be needed to establish some properties of the moduli. Steklov means and equivalent K-functionals are given.

AMS Subject Classification (1991): 46E35, 46B70, 41A10

Received January 26, 1996 and in revised form March 22, 1996. (Registered under 5720/2009.)