Parabolic maximal functions and potentials of distributions in Hp

A linear homogeneous ODE is constructed, among whose solutions are all products of solutions of two given linear homogeneous ODE's L_mu]=0, M_nv]=0, in some classes. Its order is the minimum and its coefficients can be obtained by a finite number of rational operations and differentiations on the coefficients of L_m, M_n. The problem is considered (locally) both in the real and in the complex domain, around an isolated singularity. Examples are also given.