Integral formulas for a sub-Hardy Hilbert space on the ball with complete Nevanlinna-Pick reproducing kernel

We use the theory of Hilbert spaces of analytic functions on bounded symmetric domains in C-N to obtain information on the (1/(N + 1))st power of the Bergman kernel of the ball. This kernel has played recently an important and growing role in operator theory. We present several integral formulas for the Hilbert space generated by this kernel. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS