Funding Source: Austrian Science Fund (FWF)

Duration: 10.12.2012 - 09.12.2016

Principal Investigator: Olivia Constantin

Project Number: P24986 Stand-Alone-Project

The aim of this project is to investigate the following classes of operators acting on spaces of analytic functions:

- Carleson embeddings for vector-measures on vector-valued Bergman spaces;

- Integration operators on Fock spaces with radial weights

The first direction aims to provide Carleson embedding theorems for operator-valued measures, thus answering a fundamental question concerning vector-valued Bergman spaces. This problem is related to the investigation of the Bergman projection for vector-valued functions and to the study of Hankel operators with operator-valued symbols. For these two problems recent papers co-authored by the principal investigator show that, in the setting of vector-valued Bergman spaces, the scalar results have natural generalizations even in the case when the "target-space" has infinite dimension. This is in contrast to the situation on vector-valued Hardy spaces, where the analogous results fail in the infinite-dimensional case. The gained expertise makes it realistic to expect that, while the classical Carleson embedding theorem for Hardy spaces does not extend to operator-measures, an appropriate analogue of this theorem can be obtained for vector-valued Bergman spaces.The second objective is the study of Volterra-type integration operators and of generalized Cesaro operators on Fock spaces with radial weights. We are concerned with boundedness, compactness and spectral properties,building on recent progress on these problems in somewhat simpler settings. The recent contributions of the principal investigator in this direction represent a good starting point for this part of the project.The methods of investigation consist of a combination of tools from complex analysis, functional analysis, operator theory and harmonic analysis.