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Geometric and approximation properties of generalized singular integrals in the unit disk. (English) Zbl 1107.30029
Consider \(f\) to be a (normalized) function in the disk algebra. The auhors prove estimates for the error of approximation of \(f\) by certain generalized complex singular integrals of Picard-, Poisson-Cauchy- and Gauss-Weierstrass-type. The results are in terms of the \((n+1)\)-st modulus of smoothness of \(f\). Also, approximation results for vector-valued functions on the unit disk are presented.

MSC:
30E10 Approximation in the complex plane
41A25 Rate of convergence, degree of approximation
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