| Abstract : I will discuss several basic questions concerning regularity properties of solutions to the Cauchy-Riemann equations in multidimensional complex analysis, focusing on the relationship between certain natural operators associated to a domain in Cn and their counterparts on the boundary. In particular, I will explain some of the connections between the interior and tangential Cauchy-Riemann complexes when the boundary Laplacian is subelliptic, which leads in this case to a precise comparison of the Bergman and Szego projections (the orthogonal projections in L2 onto holomorphic functions and boundary values of holomorphic functions, respectively). |