Reverse estimates in growth spaces

Abstract

Let H(B d ) denote the space of holomorphic functions on the unit ball B d of $${{\mathbb{C}}^d}$$ . Given a radial doubling weight w, we construct functions $${f, g\in H(B_1)}$$ such that |f| + |g| is comparable to w. Also, we obtain similar results for B d , d ≥ 2, and for circular, strictly convex domains with smooth boundary. As an application, we study weighted composition operators and related integral operators on growth spaces of holomorphic functions.