ORLICZ SPACES AND ENDPOINT SOBOLEV-POINCARE INEQUALITIES FOR DIFFERENTIAL FORMS IN HEISENBERG GROUPS

In this paper we prove Poincare and Sobolev inequalities for differential forms in the Rumin's contact complex on Heisenberg groups. In particular, we deal with endpoint values of the exponents, obtaining finally estimates akin to exponential Trudinger inequalities for scalar function. These results complete previous results obtained by the authors away from the exponential case. From the geometric point of view, Poincare and Sobolev inequalities for differential forms provide a quantitative formulation of the vanishing of the cohomology. They have also applications to regularity issues for partial differential equations.