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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
##### Keywords:
Jackson-type estimates; complex singular integrals
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