Some spectral properties of the canonical solution operator to [formula omitted] on weighted Fock spaces

Abstract

We characterize the Schatten class membership of the canonical solution operator to ∂¯ acting on L2(e−2ϕ), where ϕ is a subharmonic function with Δϕ a doubling measure. The obtained characterization is in terms of Δϕ. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in L2(e−2ϕ).