Uniform Approximation by General Multivariate Singular Integral Operators

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


In this chapter, we present the uniform approximation properties of general multivariate singular integral operators over \({\mathbb{R}}^{N}\), N ≥ 1. We give 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 where this theory can be applied directly. This chapter relies on [2].


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Copyright information

© George A. Anastassiou 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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