General uniform approximation theory by multivariate singular integral operators


We study the uniform approximation properties of general multivariate singular integral operators on ℝN, N ≥ 1. We establish their convergence to the unit operator with rates. The estimates are pointwise and uniform. The established inequalities involve the multivariate higher order modulus of smoothness. We list the multivariate Picard, Gauss{Weierstrass, Poisson{Cauchy and trigonometric singular integral operators to which this theory can be applied directly. © Instytut Matematyczny PAN, 2012.

Publication Title

Annales Polonici Mathematici