Article ID Journal Published Year Pages File Type
4617807 Journal of Mathematical Analysis and Applications 2011 10 Pages PDF
Abstract

Let D be a bounded symmetric domain in CN and let ψ be a complex-valued holomorphic function on D. In this work, we determine the operator norm of the bounded multiplication operator with symbol ψ from the space of bounded holomorphic functions on D to the Bloch space of D when ψ fixes the origin. If no restriction is imposed on the symbol ψ, we have a formula for the operator norm when D is the unit ball or has the unit disk as a factor. The proof of this result for the latter case makes use of a minimum principle for multiply superharmonic functions, which we prove in this work. We also show that there are no isometries among the multiplication operators when the domain does not have exceptional factors or the symbol fixes the origin.

Related Topics
Physical Sciences and Engineering Mathematics Analysis