\(BMO\) and Hankel operators on Bergman spaces
Let \(\text{BMO}_ \partial^ p\) be the space of functions on the open unit ball in \(\mathbb{C}^ n\) with bounded mean oscillation in the Bergman metric defined using the volume \(L^ p\) integral. Here the author studies the structure of \(\text{BMO}_ \partial^ p\), in particular how \(\text{BMO}_ \partial^ p\) depends on \(p\). He also characterizes \(\text{BMO}_ \partial^ p\) in terms of certain Hankel operators acting on weighted Bergman \(L^ p\) spaces. Further, the author studies in parallel the companion space \(\text{VMO}_ \partial^ p\) which is the subspace of \(\text{BMO}_ \partial^ p\) generated by functions in \(C(\overline B_ n)\) and functions with compact support.
scientific article; zbMATH DE number 165402