THE DIAGONAL MAPPING IN GENERALIZED HARDY SPACES IN THE POLYDISK

摘要

Let p = (p_1,p_2), 1 < p_i < + ∞,i = 1,2, and let H~(p_1,p_2) be the Hardy class on the bidisk with a mixed norm. We give a complete discription of all holomorphic functions φ in the unit disk that are representable in the form φ(z) = f(z,z), |z| < 1, with f ∈ H~(p_1,p_2).