Title: Small Hankel operators on generalized Fock spaces,
Abstract: We consider Fock spaces $F^{p,\ell}_{\alpha}$ of entire functions on
${\mathbb C}$ associated to the weights $e^{-\alpha |z|^{2\ell}}$, where
$\alpha>0$ and $\ell$ is a positive integer. We compute explicitly the
corresponding Bergman kernel associated to $F^{2,\ell}_{\alpha}$ and, using an
adequate factorization of this kernel, we characterize the boundedness and the
compactness of the small Hankel operator $\mathfrak{h}^{\ell}_{b,\alpha}$ on
$F^{p,\ell}_{\alpha}$. Moreover, we also determine when
$\mathfrak{h}^{\ell}_{b,\alpha}$ is a Hilbert-Schmidt operator on
$F^{2,\ell}_{\alpha}$.