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.
Anastassiou, G. (2013). LP-general approximations by multivariate singular integral operators. Demonstratio Mathematica, 46 (3), 491-502. https://doi.org/10.1515/dema-2013-0475