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

Abstract

We study boundedness of the de la Vallée Poussin means V ( ) for exponential weight, for every ∈ N and every 1 ≤ ≤ ∞, where ( ) = ( )/ ( ). As an application, we obtain lim → ∞ ‖( − V ( )) / 1/4 ‖ (R) = 0 for ∈ (R).

An estimate for derivative of the de la Vallée Poussin mean

“…In [6], we proved the following; Let 1 ≤ p ≤ ∞ and w ∈ F (C 2 +). Assume that T (a n ) ≤ Cn 2/3−δ for some 0 < δ ≤ 2/3 and C > 1.…”