Distortion Properties of Holomorphic Functions of Several Complex Variables

Let Q(D) be a class of functions q, q(0) = 0, |q(z)| < 1 holomorphic in the Reinhardt domain D ? C ⁿ, a and b — arbitrary fixed numbers satisfying the condition — 1 ≤ b < a ≤ 1. ??(a, b; D) — the class of functions p such that p ? ??(a, b; D) iff for some q ? Q(D) and every z ? D. S*(a, b; D) — the class of functions f such that f ? S*(a, g; D) iff S^c(a, b; D) — the class of functions q such that q ? S^c(a, b; D) iff , where p ε ??(a, b; D) and K is an operator of the form for z=z₁,z₂,…z_n. The author obtains sharp bounds on |p(z)|, f(z)| g(z)| as well as sharp coefficient inequalities for functions in ??(a, b; D), S*(a, b; D) and S^c(a, b; D).