Holomorphic Jackson's theorems in polydiscs

The purpose of this article is to establish Jackson-type inequality in the polydiscs UN of CN for holomorphic spaces X, such as Bergman-type spaces, Hardy spaces, polydisc algebra and Lipschitz spaces. Namely,Ek⇒(f,X)≲ω1/k→,f,X,where Ek⇒(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 ω(1/k→,f,X) is the corresponding modulus of continuity.