Holomorphic Jackson's theorems in polydiscs

The purpose of this article is to establish Jackson-type inequality in the polydiscs UN of C for holomorphic spaces X, such as Bergman-type spaces, Hardy spaces, polydisc algebra and Lipschitz spaces. Namely, E k(f,X) (−→ 1/k, f,X ) , where E k(f,X) is the deviation of the best approximation of f ∈ X by polynomials of degree at most kj about the jth variable zj with respect to the X-metric and ( −→ 1/k, f,X) is the corresponding modulus of continuity. © 2005 Elsevier Inc. All rights reserved. MSC: primary 41A17; secondary 32A36