Hochschild cohomology groups of certain algebras of analytic functions with coefficients in one-dimensional bimodules

We compute the algebraic and continuous Hochschild cohomology groups of certain Frechet algebras of analytic functions on a domain U in C-n With coefficients in one-dimensional bimodules. Among the algebras considered, we focus on A = A(U). For this algebra, our results apply if U is smoothly bounded and strictly pseudoconvex, or if U is a product domain.