On the Sobolev-Poincare inequality of CR-manifolds

Abstract

The purpose is to study the CR-manifold with a contact structure conformal to the Heisenberg group. In our previous work \cite{WY}, we have proved that if the $Q^{\prime }$-curvature is nonnegative, and the integral of $Q^{\prime }$-curvature is below the dimensional bound $c_1^{\prime }$, then we have the isoperimetric inequality. In this paper, we manage to drop the condition on the nonnegativity of the $Q^{\prime }$-curvature. We prove that the volume form $e^{4u}$ is a strong $A_{\infty }$ weight. As a corollary, we prove the Sobolev-Poincaré inequality on a class of CR-manifolds with integrable $Q^{\prime }$-curvature.

18 pages. arXiv admin note: text overlap with arXiv:1611.03564