Lp boundedness of (C,1) means of orthonormal expansions for general exponential weights

摘要

Let I be a finite or infinite interval, and let W:I→(0,∞). Assume that W2 is a weight, so that we may define orthonormal polynomials corresponding to W2. For f:R→R, let sm[f] denote the mth partial sum of the orthonormal expansion of f with respect to these polynomials. We investigate boundedness in weighted Lp spaces of the (C,1) means1n∑m=1nsm[f].The class of weights W2 considered includes even and noneven exponential weights.