  We compare the spaces of Hermitian Jacobi forms (HJF) of weight $k$ and
indices $1,2$ with classical Jacobi forms (JF) of weight $k$ and indices
$1,2,4$. Using the embedding into JF, upper bounds for the order of vanishing
of HJF at the origin is obtained. We compute the rank of HJF as a module over
elliptic modular forms and prove the algebraic independence of the generators
in case of index 1. Some related questions are discussed.
