On Function Spaces Properties Of Solutions Of Complex Differential Equations

The function spaces properties of solutions of complex differential equations are discussed in this thesis in two cases.Firstly,coefficients conditions for analytic solutions of(f(k))nk+Ak-1(z)(f(k-1)nk-1+…+A1(z)(f')n1+A0(z)fn0=Ak(z)to be in Hardy spaces and Bloch spaces are obtained when Aj(z)are analytic in a simple connected region with boundaries more than one point,j=0,1,…,k;Secondly,coefficients conditions for analytic solutions of f(k)+Ak-1(z)f(k-1)+…+A1(z)f'+A0(z)f=Ak(z)and nonlinear complex equations to be in Fock space are obtained when Aj(z)are analytic in the complex plane,j=0,1,…,k.This thesis include three chapters.The progress of solutions of complex differential equations is introduced on the home and abroad,the relevant notations and definitions are recalled in the chapter 1.Function spaces properties of analytic solutions of complex differential equations in simple connected region with boundaries more than one point are studied in the chapter 2.The function space properties of the analytic solutions of nonlinear differential equations and coefficients are studied in this chapter.The main methods are Holder inequality,Cauchy integral formula and so on.Function spaces properties of analytic solutions of complex differential equations on the complex plane are studied in the chapter 3.The function space properties of the analytic solutions of linear and nonlinear differential equations and coefficients are studied in this chapter.The main methods are Holder inequality,Minkowski inequality and so on.