Small Hankel operators on generalized Fock spaces

Abstract

We consider Fock spaces $F_{\alpha }^{p,\ell }$ 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 $F_{\alpha }^{2,\ell }$ and, using an adequate factorization of this kernel, we characterize the boundedness and the compactness of the small Hankel operator ${\mathfrak{h}}_{b,\alpha }^{\ell }$ on $F_{\alpha }^{p,\ell }$. Moreover, we also determine when ${\mathfrak{h}}_{b,\alpha }^{\ell }$ is a Hilbert-Schmidt operator on $F_{\alpha }^{2,\ell }$.

References in corpus (1)

• Some spectral properties of the canonical solution operator to $\bar{\partial }$ on weighted Fock spaces

Cited by in corpus (1)

• Hankel Bilinear forms on generalized Fock-Sobolev spaces on ${\mathbb{C}}^n$