  In this paper, we study free pluriharmonic functions on noncommutative balls,
and their boundary behavior. The main tools used in this study are certain
noncommutative transforms which are introduced in the present paper and which
generalize the classical transforms of Berezin, Poisson, Fantappie, Herglotz,
and Cayley. Several classical results from complex analysis have free analogues
in our noncommutative multivariable setting.
