Carleson embeddings and integration operators of Volterra type on Fock spaces

5 March 2013
Olivia Constantin
We consider spaces of entire functions that are $p$-integrable with respect to a radial weight. Such spaces are usually called Fock spaces, and a classical example is provided by the Gaussian weight. It turns out that a function belongs to some Fock space if and only if its derivative belongs to a Fock space with a (possibly) different weight. Furthermore, we characterize the Borel measures $\mu$ for which a Fock space is continuously embedded in $L^q(\mu0)$ with $q>0$. We then illustrate the applicability of these results to the study of properties such as boundedness, compactness, Schatten class membership and the invariant subspaces of integration operators of Volterra type acting on Fock spaces. (joint work with Jose Angel Pelaez)
  • Functional Analysis Seminar