Expansion of the Heisenberg Integral Mean via Iterated Kohn Laplacians: A Pizzetti-type Formula

A generalization and some applications of the so-called Pizzetti's Formula (which expresses the integral mean of a smooth function over an Euclidean ball as a power series w.r.t. the radius of the ball, having the iterated of the ordinary Laplace operator as coefficients) is given for , the Kohn Laplace operator on the Heisenberg group. A formula expressing the n-th power of is also proved. In the case of the ordinary Laplace operator, by Pizzetti's formula, we prove in a simple way that the only nonnegative polyharmonic functions are polynomials.