Sobolev space estimates for solutions of the equation ∂¯u=f on polycylinders

Abstract

In trying to improve Weinstock's results on approximation by holomorphic functions on certain product domains, we are led to estimates in Sobolev spaces for the ∂¯-operator on polycylinders for (γ,q)-forms. This generalizes our results for the same operator on polycylinders previously obtained, and can be applied to a number of other problems such as the Corona problem.