Geodesic
General uniform approximation theory by multivariate singular integral operators
George A. Anastassiou1
1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.
Annales Polonici Mathematici, Tome 103 (2012) no. 1, pp. 15-25

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We study the uniform approximation properties of general multivariate singular integral operators on $\mathbb{R}^{N}$, $N\geq1$. 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.
DOI : 10.4064/ap103-1-2
Keywords: study uniform approximation properties general multivariate singular integral operators mathbb geq establish their convergence unit operator rates estimates pointwise uniform established inequalities involve multivariate higher order modulus smoothness list multivariate picard gauss weierstrass poisson cauchy trigonometric singular integral operators which theory applied directly

George A. Anastassiou 1

1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A. 
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George A. Anastassiou. General uniform approximation theory by multivariate
  singular integral operators. Annales Polonici Mathematici, Tome 103 (2012) no. 1, pp. 15-25. doi: 10.4064/ap103-1-2

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