# On bounded mean oscillation of operator-valued functions

It is known that a Hankel operator with analytic symbol \phi is bounded on the Hardy space H^2 if and only if \phi has bounded mean oscillation. A notoriously difficult problem is to generalize this result to the setting of operator-valued symbols. In this talk we consider compositions of such Hankel operators with derivatives of positive fractional orders. It turns out that such compositions are bounded if and only if a certain Carleson embedding condition holds. We use this to derive some new properties of Carleson embeddings with operator measures.

This talk is part of the Analysis Seminar series.