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

Authors:
D. S. Lubinsky;H. P. Mashele
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA and Mathematies Department, Witwatersrand University, Wits 2050, South Africa;Department of Mathematics, Vista University, Mamelodi Campus, South Africa
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

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) means 1/n Σm=1n Sm[f]. The class of weights W2 considered includes even and noneven exponential weights.