On the Minimum Modulus of Analytic Functions of Moderate Growth in the Unit Disc

Abstract

We study the behavior of the minimum modulus of analytic functions in the unit disc in terms of ρ ∞ -order, which is the limit of the orders of L p -norms of log | f (re iθ )| over the circle as p → ∞. This concept coincides with the usual order of the maximum modulus function if the order is greater than one. New results are obtained for analytic functions of order smaller than 1.