Norm of the multiplication operators from H-infinity to the Bloch space of a bounded symmetric domain

作者：Colonna Flavia^*; Easley Glenn R; Singman David

来源：Journal of Mathematical Analysis and Applications, 2011, 382(2): 621-630.

DOI：10.1016/j.jmaa.2011.04.064

• Multiplication operators
• Bloch space
• Bounded symmetric domains
• Multiply superharmonic
• Cartan-Brelot topology

Let D be a bounded symmetric domain in C-N and let psi be a complex-valued holomorphic function on D. In this work, we determine the operator norm of the bounded multiplication operator with symbol psi from the space of bounded holomorphic functions on D to the Bloch space of D when psi fixes the origin. If no restriction is imposed on the symbol psi, 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 isometrics among the multiplication operators when the domain does not have exceptional factors or the symbol fixes the origin.

• 出版日期2011-10-15