We prove estimates, similar in form to the classical Aleksandrov estimates,
for a Monge-Ampere type operator on the Heisenberg group. A notion of normal
mapping does not seem to be available in this context and the method of proof
uses integration by parts and oscillation estimates that lead to the
construction of an analogue of Monge-Ampere measures for convex functions in
the Heisenberg group.Comment: The results in this paper and the ideas of their proofs have been
presented in the following talks: Analysis Seminar, Temple U., October 2002;
Fabes--Chiarenza Lectures at Siracusa, December 2002; Pan-American
Conference, Santiago de Chile, January 2003; Analysis Seminar, U. of Bologna,
March 2003; and Analysis Seminar, U. Texas at Austin, March 200
