The de la Vallée Poussin Mean and Polynomial Approximation for Exponential Weight

摘要

We studyLpboundedness of the de la Vallée Poussin meansvn(f)for exponential weightw(x)=exp(-Q(x))onR. Our main result isvn(f)(w/T1/4)Lp(R)≤C∥fw∥Lp(R),for everyn∈Nand every1≤p≤∞, whereT(x)=xQ′(x)/Q(x). As an application, we obtainlimn→∞(f-vn(f))w/T1/4Lp(R)=0forfw∈Lp(R).