Approximation properties of generalized Bochner-Riesz means in the Hardy spaces Hp, 0 < p ≤ 1

摘要

A test for the convergence of the generalized spherical and ?1 Bochner-Riesz means in the Hardy spaces Hp (Dn), 0 < p ≤ 1, is obtained, where Dn is the unit polydisc. Precise orders of the approximation of functions by the generalized ?q Bochner-Riesz means in terms of the K-functional and special moduli of smoothness are found.