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On the boundedness of de la Vallée Poussin operators. (English) Zbl 1090.41501

East J. Approx. 7, No. 4, 417-444 (2001); corrigendum ibid. 13, No. 2, 223-226 (2007).
Summary: The authors state an interesting pointwise estimate of the de la Vallée Poussin kernels corresponding to Jacobi weights. Consequently sufficient conditions are given in order that the de la Vallée Poussin operator is uniformly bounded in the \(L^p\) weighted spaces with \(1\leq p\leq\infty\). Discrete de la Vallée Poussin operators are also investigated.

MSC:

41A10 Approximation by polynomials
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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