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LetH  o  l   (  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  ∈   H  o  l   (  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.

Moduli of holomorphic functions and logarithmically convex radial weights