On maximal functions in Orlicz spaces

Let Phi(t) and Psi(t) be the functions having the representations Phi(t) = integral(0)(t)a(s)ds and Psi(t) = integral(0)(t)b(s)ds, where a(s) is a positive continuous function such that integral(1)(infinity)a(s)/sds = +infinity and b(s) is quasi-increasing, Then the maximal function Mf is a function in Orlicz space L(Phi) for all f is an element of L(Psi) if and only if there exists a positive constant c(1) such that integral(1)(s)a(t)/tdt less than or equal to c(1)b(c(1)s) for all s greater than or equal to 1.