Carleson embeddings and integration operators of Volterra type on Fock spaces

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)