Linear differential equations with solutions in the QKQK spaces

For the complex differential equationf(n)+An−1(z)f(n−1)+⋯+A1(z)f′+A0(z)f=0f(n)+An−1(z)f(n−1)+⋯+A1(z)f′+A0(z)f=0 with analytic coefficients AjAj 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 AjAj such that all solutions of the equation belong to the QKQK spaces.