Cohomology with Bounds and Carleman Estimates for the ∂̄-operator on Stein Manifolds

These theorems turned out to be very useful in complex analysis and their applications include the Levi problem with bounds and cohomology with bounds. It is, therefore, natural to seek to generalize these theorems to manifolds. In [5], Theorem 1.1 was so generalized and we generalize Theorem 1.2 in this paper. The term Carleman estimates refers to the estimates in Theorem 1.2 and we use Theorem 1.2 to obtain a Leray’s isomorphism theorem with bounds on Stein manifolds, combining with weak elliptic estimates to get the generalization of Theorem 1.2 to Stein manifolds.