Some weighted estimates for the ∂̅-equation and a finite rank theorem for Toeplitz operators in the Fock space

Journal article, 2014

We consider the ∂¯-equation in C1 in classes of functions with Gaussian decay at infinity. We prove that if the right-hand side of the equation is majorated by exp(−q|z|2), with some positive q, together with derivatives up to some order, and is orthogonal, as a distribution, to all analytical polynomials, then there exists a solution with decays, together with derivatives, as exp(−q′|z|2), for any q′

Toeplitz operators d-bar equaion