Nonhomogeneous div-curl type estimates for system of complex vector fields on local Hardy spaces

In this work, we present a nonhomogeneous version of the classical div-curl type estimates in the setup of elliptic system of complex vector fields with constant coefficients on local Hardy space $h^1$. As an application, we obtain a decomposition of the local $bmo$ space via a family of vector fields depending on div-curl terms.