Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1481-1491.

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The Growth and Conditions of Solutions in Some Function Spaces for Complex Linear Differential Equations

Weifeng Yang()   

  1. School of Computational Science and Electronics, Hunan Institute of Engineering, Hunan Xiangtan 411104
  • Received:2019-05-24 Online:2020-12-26 Published:2020-12-29
  • Supported by:
    the Hunan Provincial Natural Science Foundation(2016JJ6029);the Scientific Research Fund of Hunan Provincial Education Department(16B061)


In this paper, the relationship between the solutions and coefficients of the complex linear differential equation $f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots +A_1(z)f'+A_0(z)f=0, z\in {\mathbb D}$ is investigated. A new growth estimate of the solutions is provided. Some sufficient conditions on the coefficients are also obtained such that all solutions belong to the $H_q^\infty$ space, the $F(p, q, s)$ space and the ${\cal N}^p_\alpha$ space.

Key words: Complex linear differential equation, Weighted Hardy space, F(p, q, s) space, Growth of solution

CLC Number: 

  • O174.5