Linear differential equations with solutions in the spaces

For the complex differential equation f ( n ) + A n − 1 ( z ) f ( n − 1 ) + ⋯ + A 1 ( z ) f ′ + A 0 ( z ) f = 0 with analytic coefficients A j in the unit disk, our contribution is to build up a relationship between the coefficients and solutions of the equation. We provide conditions for coefficients A j such that all solutions of the equation belong to the Q K spaces.