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General uniform approximation theory by multivariate singular integral operators

Tom 103 / 2012

George A. Anastassiou Annales Polonici Mathematici 103 (2012), 15-25 MSC: Primary 26A15, 41A17, 41A25, 41A35; Secondary 26D15, 41A36. DOI: 10.4064/ap103-1-2

Streszczenie

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.

Autorzy

  • George A. AnastassiouDepartment of Mathematical Sciences
    University of Memphis
    Memphis, TN 38152, U.S.A.
    e-mail

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