Moduli of holomorphic functions and logarithmically convex radial weights

abakumov, evgeny; doubtsov, evgueni;

Let Hol(D) denote the space of holomorphic functions on the unit disk D. We characterize those radial weights w on D for which there exist functions f, g ∈ Hol(D) such that the sum |f| + |g| is equivalent to w. Also, we obtain similar results in several complex variables for circular, strictly convex domains with smooth boundary.