Hilbert quasimodular forms and Hilbert Jacobi-like forms

Quasimodular forms and Jacobi-like forms generalize modular forms and Jacobi forms, respectively, and Hilbert quasimodular forms and Hilbert Jacobilike forms are their extensions to several variables. They are linked to each other due to the fact that each coefficient of a Hilbert Jacobi-like form is a Hilbert quasimodular form. Given a Hilbert quasimodular form, we construct a Hilbert Jacobi-like form which has the given function as one of its coefficients. The resulting Hilbert Jacobi-like form generalizes the Cohen-Kuznetsov lifting of a modular form.