Weighted Hadamard
products of holomorphic functions in the unit ball B of ℂn are studied, and are
used to establish multiplier theorems for spaces of such functions on B. An
interesting feature of such a product of two holomorphic functions f and g
on B is that it is holomorphic on the unit polydisk Un. Moreover, if, in
addition, f belongs to the Hardy space H1(B) and g belongs to the Bloch
space ℬ(B), then the non-weighted Hadamard product of f and g belongs to
BMOA(Un), the space of holomorphic functions in Un with bounded mean
oscillation on the tours (∂U)n. Refinements of this result, as well as new
charaterizations of spaces of multipliers of holomorphic functions in B, are also
established.
