Complex Linear Differential Equations And Q_K Type Spaces

For the complex differential equation with analytic coefficients Aj(j=0,1,…,n-1) in the unit disk, the situation that all solutions of the equation belong to the Qk spaces is studied in[6].This paper extends the conclusion of [6] to the QK type spaces,then investigates the growth of the coefficients Aj of the linear differential equation.The first part of the paper provides the difinitions of some function spaces such as QK space, QK type space, weighted Hardy space etc.; also provides some related basic knowledge and existed results.The second part of the paper proves that all solutions of the equation belong to the QK type spaces when the coefficients Aj(j= 0,1,…,n-1) satisfy some limited conditionsThe third part of the paper is some thoughts to some papers and books.