ON EXISTENCE OF MAIN POLYNOMIAL FOR ANALYTIC VECTOR-VALUED FUNCTIONS OF BOUNDED L-INDEX IN THE UNIT BALL

In this paper, we present necessary and sufficient conditions of boundedness of L-index in joint variables for vector-functions analytic in the unit ball, where L = (l1, l2) : B → R+ is a positive continuous vector-function, B = {z ∈ C : |z| = √ |z1| + |z2| ≤ 1}. These conditions describe local behavior of homogeneous polynomials (so-called a main polynomial) with power series expansion for analytic vector-valued functions in the unit ball. These results use a bidisc exhaustion of a unit ball.