Sharp inequalities for convolution-type operators


Let μ be a probability measure on [- a, a], a > 0, and let x0ε{lunate}[- a, a], f ε{lunate} Cn([-2a, 2a]), n ≥ 0 even. Using moment methods we derive best upper bounds to |∫-aa ( [f(x0 + y) + f(x0 - y)] 2) μ(dy) - f(x0)|, leading to sharp inequalities that are attainable and involve the second modulus of continuity of f(n) or an upper bound of it. © 1989.

Publication Title

Journal of Approximation Theory