Abstract. We study the solution of the∂-Neumann problem on (0, 1)-forms on the product of two half-planes in C 2 . In, particular, we show the solution can be decomposed into functions smooth up to the boundary and functions which are singular at the singular points of the boundary. Furthermore, we show the singular functions are log and arctan terms.

Abstract. In this paper we study the behavior of the solution to the∂-Neumann problem for (0, 1)-forms on a bi-disc in C 2 . We show singularities which arise at the distinguished boundary are of logarithmic and arctangent type.

We consider the Bergman projection on Henkin-Leiterer domains, bounded strictly pseudoconvex domains which have defining functions whose gradient is allowed to vanish. Our result describes the mapping properties of the Bergman projection between weighted L p spaces, with the weights being powers of the gradient of the defining function.

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