Uniform convergence with rates of smooth Gauss-Weierstrass singular integral operators
Abstract
In this article, we introduce and study the smooth Gauss-Weierstrass singular integral operators on the line of very general kind. We establish their convergence to the unit operator with rates. The estimates are mostly sharp and they are pointwise or uniform. The established inequalities involve the higher order modulus of smoothness. To prove optimality we use mainly the geometric moment theory method. © 2009 Taylor & Francis.
Publication Title
Applicable Analysis
Recommended Citation
Anastassiou, G., & Mezei, R. (2009). Uniform convergence with rates of smooth Gauss-Weierstrass singular integral operators. Applicable Analysis, 88 (7), 1015-1037. https://doi.org/10.1080/00036810903114809
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