LP-general approximations by multivariate singular integral operators


In this article, we study the Lp, 1 ≤ p < ∞ approximation properties of general multivariate singular integral operators over RN, N ≥ 1. We establish their convergence to the unit operator with rates. 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 where this theory can be applied directly.

Publication Title

Demonstratio Mathematica