Carleson embeddings and integration operators of Volterra type on Fock spaces
Abstract
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)