Abstract

Let I be a finite or infinite interval, and let W : I→(0,∞) . Assume that W 2 is a weight, so that we may define orthonormal polynomials corresponding to W 2. For f : R→ R , let s m [ f] denote the mth partial sum of the orthonormal expansion of f with respect to these polynomials. We investigate boundedness in weighted L p spaces of the ( C,1) means 1 n ∑ m=1 n s m[f]. The class of weights W 2 considered includes even and noneven exponential weights.

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