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We study the uniform approximation properties of general multivariate singular integral operators on , N ≥ 1. 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.
We investigate generalized Bochner-Riesz means at the critical index on spaces generated by smooth blocks and give some approximation theorems.
In the present paper, we prove a global direct theorem for the modified Baskakov type operators in terms of so called Ditzian-Totik modulus of smoothness.
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