H(⊗1 C+) denotes the Hardy space of square integrable functions analytic in each variable separately. Let P be the natural projection of L(⊗1 C+) onto H (⊗1 C+). A Hankel operator with symbol b is the linear operator from H(⊗1 C+) to H (⊗1 C+) given by Hb φ = P⊖bφ. We show that ‖Hb‖ ≃ ‖P b‖BMO(⊗n 1 C+) , where the right hand norm is S.-Y. Chang and R. Fefferman product BMO. This fact has well k...

It is a classical fact that there is no Riemann mapping theorem in the function theory of several complex variables. Indeed, H. Poincaré proved in 1906 that the unit ball B = {z = (z1, z2) ∈ C 2 : |z| ≡ |z1| 2 + |z2| 2 < 1} and the unit bidisc D = {z = (z1, z2) ∈ C 2 : |z1| < 1, |z2| < 1} are biholomorphically inequivalent. More recently, Burns/Shnider/Wells [BSW] and Greene/Krantz [GRK1] have ...

We will make some comment on the following recent result of J. J. Kohn. In the complex space Cn:(z1, . . . , zn) if fl, . . . , fn are holomorphic in the unit ball and have continuous boundary values on the boundary, and if on the boundary the linear combination 1fi+ + j,,f is 0, then the functions fl, . .. , f,, are identically 0. 1. We denote by D any bounded circular domain in C., by B its b...

The purpose of this article is to describe three recent structure theorems in the theory of several complex variables and to point out a few of the many applications of these three theorems. In the first section we discuss a characterization of those currents (defined on an open subset of C) which correspond to integration over complex subvarieties. The second section is concerned with the stru...

0. Introduction. Geometric analysis in several complex variables and Cauchy Riemann geometry has been a quite active subject in pure and applied mathematics for decades. The classical work of Poincaré, Hartogs, Levi, E. Cartan, etc at the beginning of the century laid down part of the frame work of such a study. Since then, more and more attention has be paid to this field, as people discover i...