Moduli of holomorphic functions and logarithmically convex radial weights

Abstract

Let $H(D)$ denote the space of holomorphic functions on the unit disk $D$. We characterize those radial weights $w$ on $D$, for which there exist functions $f,g\in H(D)$ 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.

14 pages, 1 figure; section 4 is rewritten

Cited by in corpus (6)

• On inclusion relations between weighted spaces of entire functions
• Harmonic approximation by finite sums of moduli
• Optimal Domain of generalized Volterra operators
• On strong growth conditions for weighted spaces of entire functions
• Embedding theorems for Bergman-Zygmund spaces induced by doubling weights
• Gaussian analytic functions and operator symbols of Dirichlet type